Journal
GEOMETRIC AND FUNCTIONAL ANALYSIS
Volume 30, Issue 5, Pages 1337-1369Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00039-020-00547-z
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Funding
- NSERC Discovery grant [502617-2017]
- ERC [692925 NUHGD]
- National Science Foundation [DMS-2000167]
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Given an integer k >= 5, and a C-k Anosov flow F on some compact connected 3-manifold preserving a smooth volume, we show that the measure of maximal entropy is the volume measure if and only if Phi is Ck-epsilon-conjugate to an algebraic flow, for epsilon > 0 arbitrarily small. Moreover, in the case of dispersing billiards, we show that if the measure of maximal entropy is the volume measure, then the Birkhoff Normal Form of regular periodic orbits with a homoclinic intersection is linear.
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