Periodic orbits in Roessler system

Abstract: In a joint work with Piotr Zgliczynski, we study the Roessler system with an attracting periodic orbit, for two sets of parameters. In both cases the attractor on a Poincare section seems to be almost one-dimensional and therefore we apply the methods for two-dimensional perturbations of an interval's self-map introduced by Zgliczynski in Multidimensional perturbations of one-dimensional maps and stability of Sharkovskii ordering in 1999. We prove the existence of p-periodic orbits for almost all natural p with computer assistance: by interval Newton method and covering relations.

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

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