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

Pages: 701 - 708, Issue Special, July 2003

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Paweł Pilarczyk - Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072 Kraków, Poland (email)

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.

Keywords:  Conley index, periodic orbit, RÄossler equations, isolating neighbor-hood, algorithm.
Mathematics Subject Classification:  Primary: 34C25; Secondary: 54H20, 65L99.

Received: September 2002; Published: April 2003.