Jan Bouwe van den Berg

Publications

Validated integration of semilinear parabolic PDEs, Jan Bouwe van den Berg, Maxime Breden and Ray Sheombarsing, preprint 2023.
Towards computational Morse-Floer homology: forcing results for connecting orbits by computing relative indices of critical points, Jan Bouwe van den Berg, Marcio Gameiro, Jean-Philippe Lessard and Rob van der Vorst, to appear in Foundations of Computational Mathematics, 2023.
Constructive proofs for localized radial solutions of semilinear elliptic systems on R^d, Jan Bouwe van den Berg, Olivier Hénot and Jean-Philippe Lessard, to appear in Nonlinearity, 2023.
Validated numerical approximation of stable manifolds for parabolic partial differential equations, Jan Bouwe van den Berg, Jonathan Jaquette and Jay Mireles James, to appear in Journal of Dynamics and Differential Equations, 2023.
More on the parameterization method for center manifolds, Jan Bouwe van den Berg, Wouter Hetebrij and Bob Rink, preprint 2020.
Large fronts in nonlocally coupled systems using Conley-Floer homology, Bente Bakker and Jan Bouwe van den Berg, Annales Henri Poincaré 24, 605-696 (2023).
A general method for computer-assisted proofs of periodic solutions in delay differential problems, Jan Bouwe van den Berg, Chris Groothedde and Jean-Philippe Lessard, Journal of Dynamics and Differential Equations 34, 853-896 (2022).
Rigorous validation of a Hopf bifurcation in the Kuramoto-Sivashinsky PDE, Jan Bouwe van den Berg and Elena Queirolo, Communications in Nonlinear Science and Numerical Simulation 108, 106-133 (2022).
Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: a Taylor-Chebyshev series approach, Jan Bouwe van den Berg, Gabriel Duchesne and Jean-Philippe Lessard, Journal of Computational Dynamics 9, 253-278 (2022).
Spontaneous periodic orbits in the Navier-Stokes flow, Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard and Lennaert van Veen, Journal of Nonlinear Science 31:41, 1-64 (2021).
Rigorous numerics for ODEs using Chebyshev series and domain decomposition, Jan Bouwe van den Berg and Ray Sheombarsing, Journal of Computational Dynamics 8, 353-401 (2021).
Rigorous verification of Hopf bifurcations via desingularization and continuation, Jan Bouwe van den Berg, Jean-Philippe Lessard and Elena Queirolo, SIAM Journal on Applied Dynamical Systems 20, 573-607 (2021).
Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem, Jan Bouwe van den Berg and JF Williams, Physca D 415, 132732, 1-23, (2021).
A general framework for validated continuation of periodic orbits in systems of polynomial ODEs, Jan Bouwe van den Berg and Elena Queirolo, J. Computational Dynamics 8, 59-97 (2021).
The parameterization method for center manifolds, Jan Bouwe van den Berg, Wouter Hetebrij and Bob Rink, J. Differential Equations 269, 2132-2184 (2020).
Validated computations for connecting orbits in polynomial vector fields, Jan Bouwe van den Berg and Ray Sheombarsing, Indag. Math. 21, 310-373 (2020).
Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions, Jan Bouwe van den Berg and JF Williams, SIAM J. Math. Anal. 51, 131-158 (2019).
A Floer homology approach to travelling waves in reaction-diffusion equations on cylinders, Bente Bakker, Jan Bouwe van den Berg and Robert C. van der Vorst, SIAM J. Appl. Dyn. Syst. 17, 2634-2706 (2018).
Introduction to rigorous numerics in dynamics: general functional analytic setup and an example that forces chaos, Jan Bouwe van den Berg, in "Rigorous numerics in dynamics", 1-25, Proc. Sympos. Appl. Math. 74, Amer. Math. Soc. (2018).
Computer-assisted proofs for radially symmetric solutions of PDEs, István Balázs, Jan Bouwe van den Berg, Julien Courtois, János Dudás, Jean-Philippe Lessard, Anett Vörös-Kiss, JF Williams and Xi Yuan Yin, J. Computational Dynamics 5, 61-80 (2018).
A proof of Wright's conjecture, Jan Bouwe van den Berg and Jonathan Jaquette, J. Differential Equations 264, 7412-7462 (2018).
Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof, Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard and Maxime Murray, J. Differential Equations 264, 3086–3130 (2018).
Validation of the bifurcation diagram in the 2D Ohta-Kawasaki problem, Jan Bouwe van den Berg and JF Williams, Nonlinearity 30, 1584-1638 (2017).
The Poincaré-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations, Jan Bouwe van den Berg, Simone Munao and Robert C. van der Vorst, Physica D 334, 19-28 (2016).
Parameterization of slow-stable manifolds and their invariant vector bundles: theory and numerical implementation, Jan Bouwe van den Berg and Jay Mireles James, Discrete and Continuous Dynamical Systems A 36, 4637-4664 (2016).
Computing (un)stable manifolds with validated error bounds: non-resonant and resonant spectra, Jan Bouwe van den Berg, Jay Mireles James and Christian Reinhardt, J. Nonlinear Science 26, 1055-1095 (2016).
Closed characteristics for non-compact mechanical contact manifolds, Jan Bouwe van den Berg, Federica Pasquotto, Thomas Rot and Robert C. van der Vorst, J. Symplectic Geometry 14, 1145-1173 (2016).
Disruptive selection as a driver of evolutionary branching and caste evolution in social insects, Robert Planqué, Scott Powell, Nigel R. Franks and Jan Bouwe van den Berg, Journal of Evolutionary Biology 29, 2111-2128 (2016).
Rigorous numerics in dynamics, Jan Bouwe van den Berg and Jean-Philippe Lessard, Notices of the AMS 62, 1057-1061 (2015).
Rigorous computation of a radially symmetric localised solution in a Ginzburg-Landau problem, Jan Bouwe van den Berg, Chris Groothedde and J.F. Williams, SIAM J. Appl. Dyn. Syst. 14, 423-447 (2015).
Stationary coexistence of hexagons and rolls via rigorous computations, Jan Bouwe van den Berg, Andréa Deschênes, Jean-Philippe Lessard and Jay Mireles James, SIAM J. Appl. Dyn. Syst. 14, 942-979 (2015).
Braid Floer homology, Jan Bouwe van den Berg, Robert Ghrist, Robert C. van der Vorst and Wojciech Wójcik, J. Differential Equations 259, 1663-1721 (2015).
Braided connecting orbits in parabolic equations via computational homology, Jan Bouwe van den Berg, Sarah Day and Robert C. van der Vorst J. Differential Equations 255, 1086-1108 (2013).
(In-)Stability of singular equivariant solutions to the Landau-Lifshitz-Gilbert equation, Jan Bouwe van den Berg and J.F. Williams, Eur. J. Applied Math. 24, 921-948 (2013).
The interplay between scent trails and group-mass recruitment systems in ants, Robert Planqué, Jan Bouwe van den Berg and Nigel R. Franks, Bull. Math. Biol. 75, 1912-1940 (2013).
Oscillatory solutions of fourth order conservative systems via the Conley index, Jan Bouwe van den Berg, Miroslav Kramár, Robert C. van der Vorst, J. Differential Equations 252, 6061-6098 (2012).
Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation, Jan Bouwe van den Berg, Jay Mireles-James, Jean-Philippe Lessard and Konstantin Mischaikow, SIAM J. Math. Anal. 43, 1557-1594 (2011).
The ordering of bifurcation points in fourth order conservative systems, Jan Bouwe van den Berg, Miroslav Kramár, Robert C. van der Vorst, SIAM J. Appl. Dyn. Syst. 10, 510-550 (2011).
Travelling waves in a radiation-combustion free-boundary model for flame propagation, Jan Bouwe van den Berg, Hala Elrofai and Josephus Hulshof, Comb. Theory. Model. 15, 1-21 (2011).
Recruitment strategies and colony size in social insects, Robert Planqué, Jan Bouwe van den Berg and Nigel R. Franks, PLoS ONE 5 (8): e11664 (2010).
Vanishing beyond all orders: Stokes lines in a water-wave model equation, Jan Bouwe van den Berg and John R. King, Nonlinearity 23, 1-21 (2010)
Global smooth solution curves using rigorous branch following, Jan Bouwe van den Berg, Jean-Philippe Lessard and Konstantin Mischaikow, Mathematics of Computation 79, 1565-1584 (2010).
Closed characteristics on non-compact hypersurfaces in R²ⁿ, Jan Bouwe van den Berg, Federica Pasquotto and Robert C. van der Vorst, Mathematische Annalen 343, 247-284 (2009).
Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation, Jan Bouwe van den Berg and Jean-Philippe Lessard, SIAM J. Appl. Dyn. Syst. 7, 988-1031 (2008).
Chaos in orientation reversing twist maps of the plane, Jan Bouwe van den Berg, Robert C. van der Vorst and Wojciech Wójcik, Topology and its Applications 154, 2580-2606 (2007).
Contact and noncontact type Hamiltonian systems generated by second order Lagrangians, Sigurd B. Angenent, Jan Bouwe van den Berg and Robert C. van der Vorst, Ergodic Theory and Dynamical Systems 27, 23-49 (2007).
Flame balls for a free boundary combustion model with radiative transfer, Jan Bouwe van den Berg, Vincent Guyonne and Josephus Hulshof, SIAM J. Appl. Math. 67, 116-137 (2006).
The speed law for highly radiative flames in a gaseous mixture with large activation energy, Jan Bouwe van den Berg, Claude-Michel Brauner, Josephus Hulshof and Alessandra Lunardi, SIAM J. Appl. Math. 66, 408-432 (2005).
The self-similar solution for draining in the thin film equation, Jan Bouwe van den Berg, Mark Bowen, John R. King and M.M.A. El-Sheikh, European J. Appl. Math. 15, 329-346 (2004).
Multiplicity and stability of travelling wave solutions in a free boundary combustion-radiation problem Olivier Baconneau, Jan Bouwe van den Berg, Claude-Michel Brauner and Josephus Hulshof, European J. Appl. Math. 15, 79-102 (2004).
Parametric dependence of exponents and eigenvalues in focussing porous media flows, Donald G. Aronson, Jan Bouwe van den Berg and Josephus Hulshof, European J. Appl. Math. 14, 85-512 (2003).
Formal asymptotics of bubbling in the harmonic map heat flow, Jan Bouwe van den Berg, Joost Hulshof and John R. King, SIAM J. Appl. Math. 63, 1682-1717 (2003).
Morse theory on spaces of braids and Lagrangian dynamics, R.W. Ghrist, J.B. van den Berg and R.C. VanderVorst, Inventiones Math. 152, 369-432 (2003).
Parameter dependence of homoclinic solutions in a single long Josephson junction, J.B. van den Berg, S.A. van Gils and T.P.P. Visser, Nonlinearity 16, 707-717 (2003).
Stable patterns for fourth order parabolic equations, J.B. van den Berg and R.C.A.M. van der Vorst, Duke Math. J. 115, 513-558 (2002).
Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations, Didier Smets and Jan Bouwe van den Berg, J. Differential Equations 184, 78-96 (2002).
Fourth order conservative Twist systems: simple closed characteristics, J.B. van den Berg and R.C.A.M. van der Vorst, Transactions AMS 354, 1383-1420 (2002).
Global branches of multi bump periodic solutions of the Swift-Hohenberg equation (big file: 1.5Mb) G.J.B. van den Berg, L.A. Peletier and W.C. Troy, Arch. Rat. Mech. Anal. 158, 91-153 (2001).
Travelling waves for fourth-order parabolic equations, Jan Bouwe van den Berg, Josephus Hulshof and Robertus van der Vorst, SIAM J. Math. Anal. 32, 1342-1374 (2001).
Closed characteristics of fourth-order Twist systems via braids, Robert W. Ghrist, Jan Bouwe van den Berg and Robert C. Vandervorst, C. R. Acad. Sci. Paris Sér. I Math. 331, 861-865 (2000).
Homotopy classes for stable periodic and chaotic patterns in fourth-order Hamiltonian systems, W.D. Kalies, J. Kwapisz, J.B. van den Berg and R.C.A.M. van der Vorst, Comm. Math. Phys. 214, 573-592 (2000).
A domain-wall between single-mode and bimodal states, J.B. van den Berg and R.C.A.M. van der Vorst, Differential Integral Equations, 13, 369-400 (2000).
The phase-plane picture for a class of fourth-order conservative differential equations, Jan Bouwe van den Berg, J. Differential Equations, 161, 110-153 (2000).
Uniqueness of solutions for the extended Fisher-Komogorov equation, Jan Bouwe van den Berg, C. R. Acad. Sci. Paris Sér. I Math., 326, 447-452 (1998).

Thesis

My thesis is available online in PDF (5.3 Mb): dyn.pdf.

home publications research teaching short cv		Publications
		Validated integration of semilinear parabolic PDEs, Jan Bouwe van den Berg, Maxime Breden and Ray Sheombarsing, preprint 2023. Towards computational Morse-Floer homology: forcing results for connecting orbits by computing relative indices of critical points, Jan Bouwe van den Berg, Marcio Gameiro, Jean-Philippe Lessard and Rob van der Vorst, to appear in Foundations of Computational Mathematics, 2023. Constructive proofs for localized radial solutions of semilinear elliptic systems on R^d, Jan Bouwe van den Berg, Olivier Hénot and Jean-Philippe Lessard, to appear in Nonlinearity, 2023. Validated numerical approximation of stable manifolds for parabolic partial differential equations, Jan Bouwe van den Berg, Jonathan Jaquette and Jay Mireles James, to appear in Journal of Dynamics and Differential Equations, 2023. More on the parameterization method for center manifolds, Jan Bouwe van den Berg, Wouter Hetebrij and Bob Rink, preprint 2020. Large fronts in nonlocally coupled systems using Conley-Floer homology, Bente Bakker and Jan Bouwe van den Berg, Annales Henri Poincaré 24, 605-696 (2023). A general method for computer-assisted proofs of periodic solutions in delay differential problems, Jan Bouwe van den Berg, Chris Groothedde and Jean-Philippe Lessard, Journal of Dynamics and Differential Equations 34, 853-896 (2022). Rigorous validation of a Hopf bifurcation in the Kuramoto-Sivashinsky PDE, Jan Bouwe van den Berg and Elena Queirolo, Communications in Nonlinear Science and Numerical Simulation 108, 106-133 (2022). Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: a Taylor-Chebyshev series approach, Jan Bouwe van den Berg, Gabriel Duchesne and Jean-Philippe Lessard, Journal of Computational Dynamics 9, 253-278 (2022). Spontaneous periodic orbits in the Navier-Stokes flow, Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard and Lennaert van Veen, Journal of Nonlinear Science 31:41, 1-64 (2021). Rigorous numerics for ODEs using Chebyshev series and domain decomposition, Jan Bouwe van den Berg and Ray Sheombarsing, Journal of Computational Dynamics 8, 353-401 (2021). Rigorous verification of Hopf bifurcations via desingularization and continuation, Jan Bouwe van den Berg, Jean-Philippe Lessard and Elena Queirolo, SIAM Journal on Applied Dynamical Systems 20, 573-607 (2021). Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem, Jan Bouwe van den Berg and JF Williams, Physca D 415, 132732, 1-23, (2021). A general framework for validated continuation of periodic orbits in systems of polynomial ODEs, Jan Bouwe van den Berg and Elena Queirolo, J. Computational Dynamics 8, 59-97 (2021). The parameterization method for center manifolds, Jan Bouwe van den Berg, Wouter Hetebrij and Bob Rink, J. Differential Equations 269, 2132-2184 (2020). Validated computations for connecting orbits in polynomial vector fields, Jan Bouwe van den Berg and Ray Sheombarsing, Indag. Math. 21, 310-373 (2020). Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions, Jan Bouwe van den Berg and JF Williams, SIAM J. Math. Anal. 51, 131-158 (2019). A Floer homology approach to travelling waves in reaction-diffusion equations on cylinders, Bente Bakker, Jan Bouwe van den Berg and Robert C. van der Vorst, SIAM J. Appl. Dyn. Syst. 17, 2634-2706 (2018). Introduction to rigorous numerics in dynamics: general functional analytic setup and an example that forces chaos, Jan Bouwe van den Berg, in "Rigorous numerics in dynamics", 1-25, Proc. Sympos. Appl. Math. 74, Amer. Math. Soc. (2018). Computer-assisted proofs for radially symmetric solutions of PDEs, István Balázs, Jan Bouwe van den Berg, Julien Courtois, János Dudás, Jean-Philippe Lessard, Anett Vörös-Kiss, JF Williams and Xi Yuan Yin, J. Computational Dynamics 5, 61-80 (2018). A proof of Wright's conjecture, Jan Bouwe van den Berg and Jonathan Jaquette, J. Differential Equations 264, 7412-7462 (2018). Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof, Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard and Maxime Murray, J. Differential Equations 264, 3086–3130 (2018). Validation of the bifurcation diagram in the 2D Ohta-Kawasaki problem, Jan Bouwe van den Berg and JF Williams, Nonlinearity 30, 1584-1638 (2017). The Poincaré-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations, Jan Bouwe van den Berg, Simone Munao and Robert C. van der Vorst, Physica D 334, 19-28 (2016). Parameterization of slow-stable manifolds and their invariant vector bundles: theory and numerical implementation, Jan Bouwe van den Berg and Jay Mireles James, Discrete and Continuous Dynamical Systems A 36, 4637-4664 (2016). Computing (un)stable manifolds with validated error bounds: non-resonant and resonant spectra, Jan Bouwe van den Berg, Jay Mireles James and Christian Reinhardt, J. Nonlinear Science 26, 1055-1095 (2016). Closed characteristics for non-compact mechanical contact manifolds, Jan Bouwe van den Berg, Federica Pasquotto, Thomas Rot and Robert C. van der Vorst, J. Symplectic Geometry 14, 1145-1173 (2016). Disruptive selection as a driver of evolutionary branching and caste evolution in social insects, Robert Planqué, Scott Powell, Nigel R. Franks and Jan Bouwe van den Berg, Journal of Evolutionary Biology 29, 2111-2128 (2016). Rigorous numerics in dynamics, Jan Bouwe van den Berg and Jean-Philippe Lessard, Notices of the AMS 62, 1057-1061 (2015). Rigorous computation of a radially symmetric localised solution in a Ginzburg-Landau problem, Jan Bouwe van den Berg, Chris Groothedde and J.F. Williams, SIAM J. Appl. Dyn. Syst. 14, 423-447 (2015). Stationary coexistence of hexagons and rolls via rigorous computations, Jan Bouwe van den Berg, Andréa Deschênes, Jean-Philippe Lessard and Jay Mireles James, SIAM J. Appl. Dyn. Syst. 14, 942-979 (2015). Braid Floer homology, Jan Bouwe van den Berg, Robert Ghrist, Robert C. van der Vorst and Wojciech Wójcik, J. Differential Equations 259, 1663-1721 (2015). Braided connecting orbits in parabolic equations via computational homology, Jan Bouwe van den Berg, Sarah Day and Robert C. van der Vorst J. Differential Equations 255, 1086-1108 (2013). (In-)Stability of singular equivariant solutions to the Landau-Lifshitz-Gilbert equation, Jan Bouwe van den Berg and J.F. Williams, Eur. J. Applied Math. 24, 921-948 (2013). The interplay between scent trails and group-mass recruitment systems in ants, Robert Planqué, Jan Bouwe van den Berg and Nigel R. Franks, Bull. Math. Biol. 75, 1912-1940 (2013). Oscillatory solutions of fourth order conservative systems via the Conley index, Jan Bouwe van den Berg, Miroslav Kramár, Robert C. van der Vorst, J. Differential Equations 252, 6061-6098 (2012). Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation, Jan Bouwe van den Berg, Jay Mireles-James, Jean-Philippe Lessard and Konstantin Mischaikow, SIAM J. Math. Anal. 43, 1557-1594 (2011). The ordering of bifurcation points in fourth order conservative systems, Jan Bouwe van den Berg, Miroslav Kramár, Robert C. van der Vorst, SIAM J. Appl. Dyn. Syst. 10, 510-550 (2011). Travelling waves in a radiation-combustion free-boundary model for flame propagation, Jan Bouwe van den Berg, Hala Elrofai and Josephus Hulshof, Comb. Theory. Model. 15, 1-21 (2011). Recruitment strategies and colony size in social insects, Robert Planqué, Jan Bouwe van den Berg and Nigel R. Franks, PLoS ONE 5 (8): e11664 (2010). Vanishing beyond all orders: Stokes lines in a water-wave model equation, Jan Bouwe van den Berg and John R. King, Nonlinearity 23, 1-21 (2010) Global smooth solution curves using rigorous branch following, Jan Bouwe van den Berg, Jean-Philippe Lessard and Konstantin Mischaikow, Mathematics of Computation 79, 1565-1584 (2010). Closed characteristics on non-compact hypersurfaces in R²ⁿ, Jan Bouwe van den Berg, Federica Pasquotto and Robert C. van der Vorst, Mathematische Annalen 343, 247-284 (2009). Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation, Jan Bouwe van den Berg and Jean-Philippe Lessard, SIAM J. Appl. Dyn. Syst. 7, 988-1031 (2008). Chaos in orientation reversing twist maps of the plane, Jan Bouwe van den Berg, Robert C. van der Vorst and Wojciech Wójcik, Topology and its Applications 154, 2580-2606 (2007). Contact and noncontact type Hamiltonian systems generated by second order Lagrangians, Sigurd B. Angenent, Jan Bouwe van den Berg and Robert C. van der Vorst, Ergodic Theory and Dynamical Systems 27, 23-49 (2007). Flame balls for a free boundary combustion model with radiative transfer, Jan Bouwe van den Berg, Vincent Guyonne and Josephus Hulshof, SIAM J. Appl. Math. 67, 116-137 (2006). The speed law for highly radiative flames in a gaseous mixture with large activation energy, Jan Bouwe van den Berg, Claude-Michel Brauner, Josephus Hulshof and Alessandra Lunardi, SIAM J. Appl. Math. 66, 408-432 (2005). The self-similar solution for draining in the thin film equation, Jan Bouwe van den Berg, Mark Bowen, John R. King and M.M.A. El-Sheikh, European J. Appl. Math. 15, 329-346 (2004). Multiplicity and stability of travelling wave solutions in a free boundary combustion-radiation problem Olivier Baconneau, Jan Bouwe van den Berg, Claude-Michel Brauner and Josephus Hulshof, European J. Appl. Math. 15, 79-102 (2004). Parametric dependence of exponents and eigenvalues in focussing porous media flows, Donald G. Aronson, Jan Bouwe van den Berg and Josephus Hulshof, European J. Appl. Math. 14, 85-512 (2003). Formal asymptotics of bubbling in the harmonic map heat flow, Jan Bouwe van den Berg, Joost Hulshof and John R. King, SIAM J. Appl. Math. 63, 1682-1717 (2003). Morse theory on spaces of braids and Lagrangian dynamics, R.W. Ghrist, J.B. van den Berg and R.C. VanderVorst, Inventiones Math. 152, 369-432 (2003). Parameter dependence of homoclinic solutions in a single long Josephson junction, J.B. van den Berg, S.A. van Gils and T.P.P. Visser, Nonlinearity 16, 707-717 (2003). Stable patterns for fourth order parabolic equations, J.B. van den Berg and R.C.A.M. van der Vorst, Duke Math. J. 115, 513-558 (2002). Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations, Didier Smets and Jan Bouwe van den Berg, J. Differential Equations 184, 78-96 (2002). Fourth order conservative Twist systems: simple closed characteristics, J.B. van den Berg and R.C.A.M. van der Vorst, Transactions AMS 354, 1383-1420 (2002). Global branches of multi bump periodic solutions of the Swift-Hohenberg equation (big file: 1.5Mb) G.J.B. van den Berg, L.A. Peletier and W.C. Troy, Arch. Rat. Mech. Anal. 158, 91-153 (2001). Travelling waves for fourth-order parabolic equations, Jan Bouwe van den Berg, Josephus Hulshof and Robertus van der Vorst, SIAM J. Math. Anal. 32, 1342-1374 (2001). Closed characteristics of fourth-order Twist systems via braids, Robert W. Ghrist, Jan Bouwe van den Berg and Robert C. Vandervorst, C. R. Acad. Sci. Paris Sér. I Math. 331, 861-865 (2000). Homotopy classes for stable periodic and chaotic patterns in fourth-order Hamiltonian systems, W.D. Kalies, J. Kwapisz, J.B. van den Berg and R.C.A.M. van der Vorst, Comm. Math. Phys. 214, 573-592 (2000). A domain-wall between single-mode and bimodal states, J.B. van den Berg and R.C.A.M. van der Vorst, Differential Integral Equations, 13, 369-400 (2000). The phase-plane picture for a class of fourth-order conservative differential equations, Jan Bouwe van den Berg, J. Differential Equations, 161, 110-153 (2000). Uniqueness of solutions for the extended Fisher-Komogorov equation, Jan Bouwe van den Berg, C. R. Acad. Sci. Paris Sér. I Math., 326, 447-452 (1998). Thesis My thesis is available online in PDF (5.3 Mb): dyn.pdf.