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2003, 2003(Special): 701-708. doi: 10.3934/proc.2003.2003.701

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, Poland

Received  September 2002 Published  April 2003

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: algorithm., periodic orbit, Conley index, RÄossler equations, isolating neighbor-hood.
Mathematics Subject Classification: Primary: 34C25; Secondary: 54H20, 65L9.
Citation: Paweł Pilarczyk. Topological-numerical approach to the existence of periodic trajectories in ODE's. Conference Publications, 2003, 2003 (Special) : 701-708. doi: 10.3934/proc.2003.2003.701
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