CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

January 26, 2021 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Periodic orbits in Rössler system

Seminar presented by Anna Gierzkiewicz (Agriculture University in Krakow, Poland)

In a joint work with Piotr Zgliczynski, we study the Rössler 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.