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math.DS2021
From the Sharkovskii theorem to periodic orbits for the Rössler system
Anna Gierzkiewicz, Piotr Zgliczyński
We extend Sharkovskii's theorem to the cases of -dimensional maps which are close to 1D maps, with an attracting -periodic orbit. We prove that, with relatively weak topologi…
math.DS2021
A computer-assisted proof of the existence of Smale horseshoe for the folded-towel map
Anna Gierzkiewicz
The paper contains a rigorous proof of existence of symbolic dynamics chaos in the generalized Hénon map's 4th iterate , which was conjectured in the paper \textit{A 3D Smale…
math.DS2021★ 8 cited
Periodic orbits in Rössler system
Anna Gierzkiewicz, Piotr Zgliczyński
We prove the existence of -periodic orbits for almost all in the Rössler system with attracting periodic orbit, for two sets of parameters. The proofs are compu…