Dynamics of Partial Differential Equations

Volume 5 (2008)

Number 3

The existence of chaos in infinite dimensional non-resonant systems

Pages: 185 – 209

DOI: https://dx.doi.org/10.4310/DPDE.2008.v5.n3.a1

Authors

Michal Fečkan (Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Bratislava, Slovakia)

Joseph Gruendler

Abstract

This work is concerned with showing the existence of chaotic dynamics in the flow generated by an infinite system of strongly coupled ordinary differential equations with a finite dimensional hyperbolic part and an infinite dimensional center part. This theory can be applied to partial differential equations by using a Galerkin expansion which is illustrated by the problem of oscillations of a buckled elastic beam.

Keywords

differential equations, homoclinic solutions, bifurcations, center manifold, chaos

2010 Mathematics Subject Classification

34C37, 35Bxx, 74H65

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Published 1 January 2008