A note on partially hyperbolic systems with mostly expanding centers
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- by Zeya Mi, Yongluo Cao and Dawei Yang PDF
- Proc. Amer. Math. Soc. 145 (2017), 5299-5313 Request permission
Abstract:
We show the existence and finiteness of SRB (Physical) measures for partially hyperbolic diffeomorphism $f$ with dominated splitting $TM=E^u\oplus E^{cu}\oplus E^{cs}$, such that $(f,E^{cu})$ has the $\mathcal {G}^{+}$ property and $(f, E^{cs})$ has the $\mathcal {G}^{-}$ property.References
- José F. Alves, Christian Bonatti, and Marcelo Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math. 140 (2000), no. 2, 351–398. MR 1757000, DOI 10.1007/s002220000057
- J. Alves, C. Dias, S. Luzzatto and V. Pinheiro, SRB measures for partially hyperbolic systems whose central direction is weakly expanding: arXiv:1403.2937.
- M. Andersson and C. Vásquez, On mostly expanding diffeomorphisms: arXiv:1512.01046.
- Christian Bonatti, Lorenzo J. Díaz, and Marcelo Viana, Dynamics beyond uniform hyperbolicity, Encyclopaedia of Mathematical Sciences, vol. 102, Springer-Verlag, Berlin, 2005. A global geometric and probabilistic perspective; Mathematical Physics, III. MR 2105774
- Christian Bonatti and Marcelo Viana, SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math. 115 (2000), 157–193. MR 1749677, DOI 10.1007/BF02810585
- Rufus Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-New York, 1975. MR 0442989
- Rufus Bowen and David Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975), no. 3, 181–202. MR 380889, DOI 10.1007/BF01389848
- Ya. B. Pesin and Ya. G. Sinaĭ, Gibbs measures for partially hyperbolic attractors, Ergodic Theory Dynam. Systems 2 (1982), no. 3-4, 417–438 (1983). MR 721733, DOI 10.1017/S014338570000170X
- David Ruelle, A measure associated with axiom-A attractors, Amer. J. Math. 98 (1976), no. 3, 619–654. MR 415683, DOI 10.2307/2373810
- Ja. G. Sinaĭ, Gibbs measures in ergodic theory, Uspehi Mat. Nauk 27 (1972), no. 4(166), 21–64 (Russian). MR 0399421
- Carlos H. Vásquez, Statistical stability for diffeomorphisms with dominated splitting, Ergodic Theory Dynam. Systems 27 (2007), no. 1, 253–283. MR 2297096, DOI 10.1017/S0143385706000721
- J. Yang, Entropy along expanding foliations: arXiv:1601.05504v1.
Additional Information
- Zeya Mi
- Affiliation: School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China–and–School of Mathematics and Statistics, Nanjing University of Information Sciences and Technology, Nanjing 210044, People’s Republic of China
- Email: mizeya@163.com
- Yongluo Cao
- Affiliation: School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China
- MR Author ID: 343275
- Email: ylcao@suda.edu.cn
- Dawei Yang
- Affiliation: School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China
- Email: yangdaw1981@gmail.com, yangdw@suda.edu.cn
- Received by editor(s): November 15, 2016
- Received by editor(s) in revised form: January 24, 2017
- Published electronically: September 7, 2017
- Additional Notes: The first author would like to thank the support of NSFC 11671288
The second author would like to thank the support of NSFC 11125103
The third author would like to thank the support of NSFC 11271152, NSFC 11671288
The authors were partially supported by A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) - Communicated by: Yingfei Yi
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5299-5313
- MSC (2010): Primary 37D30
- DOI: https://doi.org/10.1090/proc/13701
- MathSciNet review: 3717958