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Unstable entropy in smooth ergodic theory*AT is supported by FAPESP 2017/06463-3 and CNPq (PQ) 303025/2015-8. This work was finalized when the author visited Peking University and Université Paris-Sud (financial support: project ANR-16-CE40-0013 ISDEEC). The conversations with Sylvain Crovisier, Jiagang Yang, Mauricio Poletti and Jérôme Buzzi, were very useful for improving the results and I thank them. I would like to thank Yi Shi, Jinhua Zhang and the whole dynamical system group in Beijing and Suzhou for discussions during the minicourse and seminars. (19th July 2021)
Record Type:
Journal Article
Title:
Unstable entropy in smooth ergodic theory*AT is supported by FAPESP 2017/06463-3 and CNPq (PQ) 303025/2015-8. This work was finalized when the author visited Peking University and Université Paris-Sud (financial support: project ANR-16-CE40-0013 ISDEEC). The conversations with Sylvain Crovisier, Jiagang Yang, Mauricio Poletti and Jérôme Buzzi, were very useful for improving the results and I thank them. I would like to thank Yi Shi, Jinhua Zhang and the whole dynamical system group in Beijing and Suzhou for discussions during the minicourse and seminars. (19th July 2021)
Main Title:
Unstable entropy in smooth ergodic theory*AT is supported by FAPESP 2017/06463-3 and CNPq (PQ) 303025/2015-8. This work was finalized when the author visited Peking University and Université Paris-Sud (financial support: project ANR-16-CE40-0013 ISDEEC). The conversations with Sylvain Crovisier, Jiagang Yang, Mauricio Poletti and Jérôme Buzzi, were very useful for improving the results and I thank them. I would like to thank Yi Shi, Jinhua Zhang and the whole dynamical system group in Beijing and Suzhou for discussions during the minicourse and seminars.
Abstract: In this survey we recall basic notions of disintegration of measures and entropy along unstable laminations. We review some roles of unstable entropy in smooth ergodic theory including the so-called invariance principle, Margulis construction of measures of maximal entropy, physical measures and rigidity. We also give some new examples and pose some open problems.