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April  2006, 14(2): 281-293. doi: 10.3934/dcds.2006.14.281

Covering relations and non-autonomous perturbations of ODEs

1. 

Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland

2. 

Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Kraków, Poland

Received  September 2003 Revised  October 2004 Published  November 2005

Covering relations are a topological tool for detecting periodic orbits, symbolic dynamics and chaotic behavior for autonomous ODE. We extend the method of the covering relations onto systems with a time dependent perturbation. As an example we apply the method to non-autonomous perturbations of the Rössler equations to show that for small perturbation they possess symbolic dynamics.
Citation: Maciej J. Capiński, Piotr Zgliczyński. Covering relations and non-autonomous perturbations of ODEs. Discrete & Continuous Dynamical Systems - A, 2006, 14 (2) : 281-293. doi: 10.3934/dcds.2006.14.281
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