Dynamics of Endomorphisms of Lie Groups

Details Dynamics of Endomorphisms of Lie Groups Dynamics of Endomorphisms of Lie Groups

2011-05-22

arxiv.org/abs/1105.4344v1

Mathematics

Dynamical Systems

Scientific paper

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. We also characterize the recurrent and chain-recurrent sets of linear isomorphisms of finite dimensional vector spaces and of surjective endomorphisms of linear semi-simple Lie groups.

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