DCDS
Expansion growth, entropy and invariant measures of distal groups and pseudogroups of homeo- and diffeomorphisms
Paweł G. Walczak
Discrete & Continuous Dynamical Systems - A 2013, 33(10): 4731-4742 doi: 10.3934/dcds.2013.33.4731
We estimate expansion growth types (in the sense of Egashira) of certain distal groups of homeomorphisms and manifold diffeomorphisms.The estimate implies zero entropy (in the sense of Ghys, Langevin and the author) and existence of invariant measures for such groups. We prove also existence of invariant measures for pseudogroups satisfying some conditions of distality type.
keywords: invariant measures Expansion growth entropy transformatios groups.

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