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arXiv · 1105.4344

Entropy of Endomorphisms of Lie Groups

André Caldas·Mauro Patrão
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Abstract

We show, when $G$ is a nilpotent or reductive Lie group, that the entropy of any surjective endomorphism coincides with the entropy of its restriction to the toral component of the center of $G$. In particular, if $G$ is a semi-simple Lie group, the entropy of any surjective endomorphism always vanishes. Since every compact group is reductive, the formula for the entropy of a endomorphism of a compact group reduces to the formula for the entropy of an endomorphism of a torus.

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André Caldas, Mauro Patrão. 2011-05-22. Entropy of Endomorphisms of Lie Groups. https://arxiv.org/abs/1105.4344

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