Entropy for smooth abelian actions

Fried, David

doi:10.1090/S0002-9939-1983-0677244-7

Entropy for smooth abelian actions
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by David Fried

Proc. Amer. Math. Soc. 87 (1983), 111-116

DOI: https://doi.org/10.1090/S0002-9939-1983-0677244-7

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Abstract:

We generalize the usual notions of metric and topological entropy for flows to actions of compactly generated abelian Lie groups. Unlike previous generalizations, ours is nontrivial for smooth actions of ${{\mathbf {R}}^n}$, $n \geqslant 2$. We prove some elementary properties of our definitions and we relate them to characteristic exponents and the entropy conjecture.

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