Rigidity of measures on the torus: smooth stabilizers and entropy

Details Rigidity of measures on the torus: smooth stabilizers and entropy Rigidity of measures on the torus: smooth stabilizers and entropy

2010-08-19

arxiv.org/abs/1008.3197v3

Mathematics

Dynamical Systems

1 Figure

Scientific paper

For a nonlinear Anosov diffeomorphism of the 2-torus, we present examples of
measures so that the group of $\mu$-preserving diffeomorphisms is, up to
zero-entropy transformations, cyclic. For families of equilibrium states $\mu$,
we strengthen this to show that the group of $\mu$-preserving diffeomorphism is
virtually cyclic.

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