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arXiv · 1311.0213

Polynomial entropy for the circle homeomorphisms and for $C^1$ nonvanishing vector fields on $\T^2$

Clémence Labrousse
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Abstract

We prove that the polynomial entropy of an orientation preserving homeomorphism of the circle equals 1 when the homeomorphism is not conjugate to a rotation and that it is 0 otherwise. In a second part we prove that the polynomial entropy of a flow on the two dimensional torus associated with a $C^1$ nonvanishing vector field is less that $1$. We moreover prove that when the flow possesses periodic orbits its polynomial entropy equals 1 unless it is conjugate to a rotation (in this last case, the polynomial entropy is zero).

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Clémence Labrousse. 2013-11-01. Polynomial entropy for the circle homeomorphisms and for $C^1$ nonvanishing vector fields on $\T^2$. https://arxiv.org/abs/1311.0213

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