Nonlinear Dynamics at the Free University Berlin

Dr. Karsten Matthies

New web-page in Bath

Old web-page until August 2005:

Research interests

  • Averaging and Homogenization for PDE
  • Lattice dynamics
  • Homoclinic and heteroclinic bifurcations
  • Exponentially small effects

Old Projects

Old Teaching

Preprints and Publications (updated until Aug 2005)

Karsten Matthies
The Bogdanov-Takens Bifurcation implies Chaos in Dynamical Systems with D3 Symmetry
Diplomarbeit, 1996
Karsten Matthies
A subshift of finite type in the Bogdanov-Takens bifurcation with D_{3} symmetry
Doc. Math. J. DMV 4(1999), 463 -485.
Karsten Matthies
Time-Averaging of parabolic partial differential equations: exponential estimates
Dissertation FU Berlin, 1999
Karsten Matthies
Time-Averaging under Fast Periodic Forcing of Parabolic Partial Differential Equations: Exponential Estimates
Journal of Differential Equations 174 (2001), 133-180.
Short version in Proceedings of Equadiff 99, B. Fiedler, K. Gröger, and J. Sprekels (eds.), World Scientific Publishing, Singapore (2000), 952-954.
Gero Friesecke, Karsten Matthies
Atomic-scale localization of high-energy solitary waves on lattices
Physica D 171 (2002), 211-220.
Karsten Matthies
Backward error analysis of a full discretisation scheme for a class of parabolic partial differential equations
Nonlinear Anal. Theory Methods Appl. 52 (2003), 805-826.
Karsten Matthies
Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing
Discrete Contin. Dyn. Syst. 9 (2003), 585-602.
Karsten Matthies, Arnd Scheel
Exponential Averaging of Hamiltonian Evolution Equations
Trans. Amer. Math. Soc. 355 (2003), 747-773.
Gero Friesecke, Karsten Matthies
Geometric solitary waves in a 2D mass-spring lattice
Discrete Contin. Dyn. Syst. Ser. B 3 (2003), 105-114.
Karsten Matthies
Homogenisation of Exponential Order for Elliptic Systems in Infinite Cylinders
Asymptot. Anal. 43 (2005), 205-232.
Karsten Matthies
Exponential Averaging of Rapid Quasiperiodic Forcing
Preprint no 88, Schwerpunkt Multiscale Problems.
Karsten Matthies, C.E. Wayne
Wave Pinning in Strips
Preprint no 142, Schwerpunkt Multiscale Problems.
Karsten Matthies, Guido Schneider, Hannes Uecker
Exponential averaging and traveling waves in rapidly varying periodic media
Preprint no 158, Schwerpunkt Multiscale Problems (2004).
(gziped postscript)     (pdf)
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