From the Sharkovskii theorem to periodic orbits for the Rössler system

2021/06/22 by Gierzkiewicz, Anna, Zgliczyński, Piotr
#37B99 #37C27 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.11711

Abstract

We extend Sharkovskii's theorem to the cases of N-dimensional maps which are close to 1D maps, with an attracting n-periodic orbit. We prove that, with relatively weak topological assumptions, there exist also m-periodic orbits for all m\triangleright n in Sharkovskii's order, in the nearby. We also show, as an example of application, how to obtain such a result for the Rössler system with an attracting periodic orbit, for four sets of parameter values. The proofs are computer-assisted.

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