Dynamics of Partial Differential Equations
Volume 5 (2008)
The existence of chaos in infinite dimensional non-resonant systems
Pages: 185 – 209
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.
differential equations, homoclinic solutions, bifurcations, center manifold, chaos
2010 Mathematics Subject Classification
34C37, 35Bxx, 74H65