Topological-numerical approach to the existence of periodic trajectories in ODE's

Paweł Pilarczyk

doi:10.3934/proc.2003.2003.701

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2003, Volume 2003: 701-708. Doi: 10.3934/proc.2003.2003.701 open access

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Topological-numerical approach to the existence of periodic trajectories in ODE's

Paweł Pilarczyk^1,

1.
Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072 Kraków

Received: September 2002

Published: April 2003

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Abstract

We discuss an application of a topological-numerical method for proving the existence of a periodic trajectory in a smooth dynamical system in $\mathbb(R)^n$ where a periodic trajectory is numerically observed. The method is based on the Conley index theory and rigorous numerics for ODEs and it is a generalization of the method introduced in [13]. We apply this method to the Rössler equations.

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Mathematics Subject Classification: Primary: 34C25; Secondary: 54H20, 65L99.

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