8 citations · 15 across the 5 of their papers we have counts for
6 papers · 1 filter
Sharkovskii theorem for infinite dimensional dynamical systems
Anna Gierzkiewicz, Robert Szczelina
We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the sy…
No infinite spin for partial collisions converging to isolated central configurations on the plane
Anna Gierzkiewicz, Rodrigo G. Schaefer, Piotr Zgliczyński
In the -body problem, when a~cluster of bodies tends to a collision, then its normalized shape curve converges to the set of normalized central configurations, which has …
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…
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…
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…
A computer-assisted proof of symbolic dynamics in Hyperion's inner rotation model
Anna Gierzkiewicz, Piotr Zgliczyński
The rotation of Hyperion is often modelled by equations of motion of an ellipsoidal satellite. The model is expected to be chaotic for large range of parameters. The paper contains…