Maximal entropy measures of diffeomorphisms of circle fiber bundles

We characterize the maximal entropy measures of partially hyperbolic C2 diffeomorphisms whose center foliations form circle bundles, by means of suitable finite sets of saddle points, that we call skeletons. In the special case of 3‐dimensional nilmanifolds other than the torus, this entails the fol...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2021-04, Vol.103 (3), p.1016-1034
Main Authors: Ures, Raúl, Viana, Marcelo, Yang, Jiagang
Format: Article
Language:English
Subjects:
37D30 (secondary)
37D35 (primary)
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Summary:We characterize the maximal entropy measures of partially hyperbolic C2 diffeomorphisms whose center foliations form circle bundles, by means of suitable finite sets of saddle points, that we call skeletons. In the special case of 3‐dimensional nilmanifolds other than the torus, this entails the following dichotomy: either the diffeomorphism is a rotation extension of an Anosov diffeomorphism — in which case there is a unique maximal measure, with full support and zero center Lyapunov exponents — or there exist exactly two ergodic maximal measures, both hyperbolic and whose center Lyapunov exponents have opposite signs. Moreover, the set of maximal measures varies continuously with the diffeomorphism.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12399