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We study the polynomial entropy of the wandering part of any invertible dynamical system on a compact metric space. As an application we compute the polynomial entropy of Brouwer homeomorphisms (fixed point free orientation preserving homeomorphisms of the plane), and show in particular that it takes every real value greater or equal to 2.
We use the homotopy Brouwer theory of Handel to define a Poincar{e} index between two orbits for an orientation preserving fixed point free homeomorphism of the plane. Furthermore, we prove that this index is almost additive.
Homotopy Brouwer theory is a tool to study the dynamics of surface homeomorphisms. We introduce and illustrate the main objects of homotopy Brouwer theory, and provide a proof of Handels fixed point theorem. These are the notes of a mini-course held
A group $G$ is said to be periodic if for any $gin G$ there exists a positive integer $n$ with $g^n=id$. We prove that a finitely generated periodic group of homeomorphisms on the 2-torus that preserves a measure $mu$ is finite. Moreover if the group
We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincare-like classification for this class of maps of Jaeger-Stark, we demonstrate that transitive but non
A group $Gamma$ is said to be periodic if for any $g$ in $Gamma$ there is a positive integer $n$ with $g^n=id$. We first prove that a finitely generated periodic group acting on the 2-sphere $SS^2$ by $C^1$-diffeomorphisms with a finite orbit, is f