Covering relations and non-autonomous perturbations of ODEs

Maciej  J. Capiński; Piotr Zgliczyński

doi:10.3934/dcds.2006.14.281

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2006, Volume 14, Issue 2: 281-293. Doi: 10.3934/dcds.2006.14.281

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Covering relations and non-autonomous perturbations of ODEs

Maciej J. Capiński^1, and
Piotr Zgliczyński^2,

1.
Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków
2.
Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Kraków

Received: August 31, 2003

Revised: September 30, 2004

Published: March 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 37B10, 37B55; Secondary: 37B30.

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