Published articles and preprints

2019:
• Rabinowitz-Floer homology for tentacular Hamiltonians
  F. Pasquotto, R.C.A.M. Vandervorst and J. Wisnieuwska
  Preprint 2019.

2018:

• A Floer homology approach to traveling waves in reaction-diffusion equations on cylinders
  B. Bakker, J.B. van den Berg and R.C.A.M. Vandervorst
  SIAM J. Appl. Dyn. Syst. 17 (2018), no. 4, 2634-2706.
• An algorithmic approach to lattices and order in dynamics
  W.D. Kalies, D. Kasti and R.C.A.M. Vandervorst
  SIAM J. Appl. Dyn. Syst. 17 (2018), no. 2, 1617-1649.

2017:

• Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
  M. Izydorek, T.O. Rot, M. Starostka, M. Styborski and R.C.A.M. Vandervorst
  J. Differential Equations 263 (2017), no. 11, 7162-7186.
• Symplectomorphisms and discrete braid invariants
  A. Czechowski and R.C.A.M. Vandervorst
  J. Fixed Point Theory Appl. 19 (2017), no. 1, 231-262.
• The Poincaré-Hopf Theorem for relative braid classes
  S. Munao and R.C.A.M. Vandervorst
  Math. Z. 287 (2017), no. 1-2, 679-703.
• On the dynamics of second-order Lagrangian systems
  R. Adams, W.D. Kalies and R.C.A.M. Vandervorst
  Electron. J. Differential Equations 2017, Paper No. 101, 20 pp.

2016:

• Computational Conley theory
  W.D. Kalies and R.C.A.M. Vandervorst
  Nieuw Arch. Wiskd. (5) 17 (2016), no. 3, 200-206.
• Lattice structures for attractors II
  W.D. Kalies, K. Mischaikow and R.C.A.M. Vandervorst
  Found. Comput. Math. 16 (2016), no. 5, 1151-1191.
• On periodic orbits in cotangent bundles of non-compact manifolds
  J.B. van den Berg, F. Pasquotto, T.O. Rot and R.C.A.M. Vandervorst
  J. Symplectic Geom. 14 (2016), no. 4, 1145-1173.
• The Poincaré-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations
  S. Munao and R.C.A.M. Vandervorst
  Phys. D 334 (2016), 19-28.

2015:

• Braid Floer homology
  J.B. van den Berg, R.W. Ghrist, R.C.A.M. Vandervorst and W. Wojcik
  Journal of Differential Equations 259 (5) (2015), 1663-1721.

2014:

• Functoriality and Duality in Morse-Conley-Floer Homology
  T. Rot and R.C.A.M. Vandervorst
  J. Fixed Point Theory Appl. 16 (2014), no. 1-2, 437-476.
• Morse-Conley-Floer Homology
  T. Rot and R.C.A.M. Vandervorst
  J. Topol. Anal. 6 (2014), no. 3, 305-338
• Lattice structures for attractors I
  W.D. Kalies, K. Mischaikow and R.C.A.M. Vandervorst
  AIMS J. of Comp. Dyn. 1(2) (2014), 307-338.

2013:

• Braided connecting orbits in parabolic equations via computational homology
  J.B. van den Berg, S. Day and R.C.A.M. Vandervorst
  Journal of Differential Equations, Volume 255, Issue 6, Pages 1086-1108.

2012:

• Oscillatory solutions of fourth order conservative systems
  J.B. van den Berg, M. Kramar and R.C.A.M. Vandervorst
  J. Differential Equations 252 (2012), no. 11, 6061-6098.

2011:

• The order of bifurcation points in fourth order conservative systems via braids
  J.B. van den Berg, M. Kramar and R.C.A.M. Vandervorst
  SIAM J. Appl. Dyn. Syst. 10 (2011), no. 2, 510 - 550,
• Floer homology, relative braid classes, and low dimensional dynamics
  R.C.A.M. Vandervorst
  Progress in variational methods, 195 - 211, Nankai Ser. Pure Appl. Math. Theoret. Phys., 7, World Sci. Publ., Hackensack, NJ, 2011

2009:

• Scalar parabolic PDE's and braids
  R.W. Ghrist and R.C.A.M. Vandervorst
  Trans. Amer. Math. Soc. 361 (2009), 2755 - 2788 (electronically December 17, 2008).

2008:

• Closed characteristics for non-compact hypersurfaces in R^{2n}
  J.B. van den Berg, F. Pasquotto and R.C.A.M. Vandervorst
  Math. Ann. 343 (2009), no. 2, 247--284 (electronically 1432-1807, 2008).

2007:

• Contact and non-contact type Hamiltonian systems generated by second order Lagrangians
  S.B. Angenent, J.B. Van den Berg and R.C.A.M. VanderVorst
  Ergodic Theory Dynam. Systems 27 (2007), no. 1, 23--49.
• Chaos in orientation reversing twist maps of the plane
  J.B. VandenBerg, R.C. Vandervorst and W. Wojcik
  Topology Appl. 154 (2007), no. 13, 2580--2606.

2005:

• An algorithmic approach to chain recurrence
  W.D. Kalies, K. Mischaikow and R.C. Vandervorst
  Fund. Comp. Math. 5(4) (2005), 409-449.

2004:

• Closed characteristics of second order Lagrangians
  W.D. Kalies and R.C.A.M. VanderVorst
  Proc. Roy. Soc. Edinb., Sect. A 134 (2004), no. 1, 143--158.

2003:

• Morse theory on spaces of braids and Lagrangian dynamics
  R.W. Ghrist, J.B. Van den Berg and R.C.A.M. VanderVorst
  Inventiones Mathematicae, 152(2) 2003, 369-432.

2002:

• Braids and parabolic dynamics
  R.W. Ghrist and R.C.A.M. VanderVorst
  Proceedings of New Directions in Dynamics Systems: Kyoto 2002.
• Stable patterns for fourth order parabolic equations
  J.B. Van den Berg and R.C.A.M. VanderVorst
  Duke Math. Journ. 115(3) (2002).

2001:

• Fourth order conservative Twist systems: simple closed characteristics
  J.B. Van den Berg and R.C.A.M.
  VanderVorst, Trans. Amer. Math. Soc. (2001). In pdf-format.
• Traveling waves for fourth order parabolic equations
  J. Hulshof, J.B. Van den Berg and R.C.A.M. VanderVorst
  SIAM J. Math. Anal. 32(6) (2001), 1342-1374.
• Slow motion in higher-order systems and Gamma-convergence in one space dimension
  W. Kalies, T. Wanner and R. C. A. M. Van der Vorst
  Nonlinear Anal. 44 (2001), no. 1, Ser. A: Theory Methods, 33-57.

2000:

• Closed characteristics of fourth-order Twist systems via braids
  R.W. Ghrist, J.B. Van den Berg and R.C.A.M. VanderVorst
  Comptes Rendus Ac. Sc. Paris, t. 331 (2000), 861-865.
• Periodic orbits for fourth order conservative systems and a Morse type theory
  J.B. Van den Berg and R.C.A.M. VanderVorst
  Proceedings. EquaDiff '99, (World Scientific, 2000).
• A priori bounds and renormalized Morse indices of solutions of an elliptic system
  S.B. Angenent and R. C. A. M. Van der Vorst
  Ann. l'Institute Henri Poincare 17(3), (2000), 277-306.
• A domain-wall between single-mode and bimodal states
  J.B. van den Berg and R.C.A.M. Vandervorst
  Differential Integral Equations 13 (2000), no. 1-3, 369-400.
• Homotopy classes for stable periodic and chaotic patterns in fourth order Hamiltonian systems
  W. Kalies, J. Kwapisz and J.B. Van den Berg and R. C. A. M. Van der Vorst
  Comm. Math. Phys. 214 (2000), 573-592.

1999:

• A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology
  S.B. Angenent and R. C. A. M. Van der Vorst
  Math. Zeitschrift 231 (1999) 2, 203-248.

1998:

• Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria
  W. Kalies, J. Kwapisz and R. C. A. M. Van der Vorst
  Comm. Math. Phys. 193 (1998), 337-371.
• Strongly Indefinite Systems with Critical Sobolev Exponents
  J. Hulshof, E. Mitidieri and R. C. A. M. Van der Vorst
  Trans. Amer. Math. Soc. 350 (1998), 2349-2365.

1997:

• On the non-existence of homoclinic orbits for a class of infinite dimensional Hamiltonian systems
  Ph. Clement and R. C. A. M. Vandervorst
  Proc. Amer. Math. Soc. {\bf 125} (1997), 1167-1176.
• On some quasilinear systems
  I. Peral and R.C.A.M. Vandervorst
  Rocky Mount. Journ. Math. 27(3), (1997), 913-927.

1996:

• Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation
  W.D. Kalies and R.C.A.M. Vandervorst
  Journ. Diff. Eq. {\bf 131} (1996), 209-228.
• Asymptotic Behaviour of Ground States
  J. Hulshof and R. C. A. M. van der Vorst
  Proc. Amer. Math. Soc. {\bf 124} (1996), 2423-2431.

1995:

• Stationary solutions of a fourth order nonlinear diffusion equation
  L.A. Peletier, W.C. Troy and R.C.A.M. van der Vorst
  Diff. Eq. {\bf 31}(2) (1995) (Russian), 327-338.
• Non-existence theorems for systems of quasilinear partial differential equations
  E. Mitidieri, G. Sweers and R.C.A.M. Vandervorst
  Diff. \& Int. Eq. {\bf 8}(6) (1995), 1331-1354.
• On a semilinear elliptic system
  Ph. Clement and R.C.A.M. Vandervorst
  Diff. \& Int. Eq. {\bf 8}(6) (1995), 1317-1329.
• Fourth order elliptic equations with critical growth
  R.C.A.M. Vandervorst
  C.R. Acad. Sci. Paris, {\bf 320}(I) (1995), 295-299.

1994:

• Interpolation spaces for $\partial_T$-systems and applications to critical point theory
  Ph. Clement and R.C.A.M. Vandervorst
  Pan. Am. Math. Journ. {\bf 4} (1994), 1-45.

1993:

• Differential systems with a strongly indefinite variational structure
  J. Hulshof and R.C.A.M. van der Vorst
  Journ. Func. Anal. {\bf 114}(1) (1993), 32-58.
• Best constant for the embedding of the space H^2 \cap H_0^1 into L^2N/(N-4)
  R.C.A.M. van der Vorst
  Diff. \& Int. Eq. {\bf 6}(2) (1993), 259-276.
• Positive solutions of the equation \Delta u + u^p = 0 on a bounded domain
  J. Hulshof and R.C.A.M. Vandervorst
  Lecture Notes, Report W93-06, Leiden University (1993).

1992:

• Existence and non-existence of positive solutions of non-linear elliptic systems and the biharmonic equation
  L.A. Peletier and R.C.A.M. van der Vorst
  Diff. \& Int. Eq. {\bf 5}(4) (1992), 747-767.

1991:

• Variational identities and applications to differential systems
  R.C.A.M. Vandervorst
  Arch. Rat. Mech. Anal. 116 (1991), 375-398.

Last Modified on June 14, 2019