Physical measures for partially hyperbolic flows with mostly contracting centre

References

• J.F. Alves, Non-uniformly expanding dynamics: stability from a probabilistic viewpoint, Discrete Contin. Dyn. Syst. 7 (2001), pp. 363–375.
   Web of Science ®Google Scholar
• J. Alves, C. Bonatti, and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math. 140 (2000), pp. 351–398.
   Web of Science ®Google Scholar
• J. Alves, C. Dias, S. Luzzatto, and V. Pinheiro, SRB measures for partially hyperbolic systems whose central direction is weakly expanding, J. Eur. Math. Soc. 19 (2017), pp. 2911–2946.
   Web of Science ®Google Scholar
• M. Andersson, Robust ergodic properties in partially hyperbolic dynamics, Trans. Am. Math. Soc. 362 (2010), pp. 1831–1867.
   Web of Science ®Google Scholar
• M. Andersson and C. Vásquez, On mostly expanding diffeomorphisms, Ergodic Theory Dyn. Syst. 38 (2018), pp. 2838–2859.
   Web of Science ®Google Scholar
• V. Araújo, E.R. Pujals, M.J. Pacifico, and M. Viana, Singular-hyperbolic attractors are chaotic, Trans. Am. Math. Soc. 361 (2009), pp. 2431–2485.
   Web of Science ®Google Scholar
• V. Araújo, A. Souza, and E. Trindade, Upper large deviations bound for singular-hyperbolic attracting sets, J. Differ. Equ. 31(2) (2019), pp. 601–652.
   Web of Science ®Google Scholar
• V. Araújo, Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability. Available at arXiv:1901.10537v1.
   Google Scholar
• L. Barreira and Y. Pesin, Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2007.
   Google Scholar
• C. Bonatti, L. Diaz, and M. Viana, Dynamics Beyond Uniform Hyperbolicity: A Global Geometric and Probabilistic Perspective, Encyclopaedia of Mathematical Sciences, vol. 102, Springer-Verlag, Berlin, 2005.
   Google Scholar
• C. Bonatti and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math. 115 (2000), pp. 157–193.
   Web of Science ®Google Scholar
• R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, vol. 470, Springer-Verlag, Berlin, 1977.
   Google Scholar
• R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975), pp. 181–202.
   Web of Science ®Google Scholar
• K. Burns, D. Dolgopyat, Y. Pesin, and M. Pollicott, Stable ergodicity for partially hyperbolic attractors with negative central exponents, J. Mod. Dyn. 2(1) (2008), pp. 63–81.
   Web of Science ®Google Scholar
• W. Cowieson and L. Young, SRB measures as zero-noise limits, Ergodic Theory Dyn. Syst. 25 (2005), pp. 1115–1138.
   Web of Science ®Google Scholar
• S. Crovisier, D. Yang, and J. Zhang, Empirical measures of partially hyperbolic attractors, Commun. Math. Phys. 375 (2020), pp. 725–764.
   Web of Science ®Google Scholar
• D. Dolgopyat, On dynamics of mostly contracting diffeomorphisms, Commun. Math. Phys. 213 (2000), pp. 181–201.
   Web of Science ®Google Scholar
• D. Dolgopyat, M. Viana, and J. Yang, Geometric and measure-theoretical structures of maps with mostly contracting center, Commun. Math. Phys. 341 (2016), pp. 991–1014.
   Web of Science ®Google Scholar
• S. Gan, F. Yang, J. Yang, and R. Zheng, Statistical properties of physical-like measures, Nonlinearity 34(2) (2021), pp. 1014–1029.
   Web of Science ®Google Scholar
• Y. Hua, F. Yang, and J. Yang, New criterion of physical measures for partially hyperbolic diffeomorphisms, Trans. Am. Math. Soc. 373 (2020), pp. 385–417.
   Web of Science ®Google Scholar
• A. Katok, Lyapunov exponents, entropy and periodic points of diffeomorphisms, Publ. Math. IHES 51 (1980), pp. 137–173.
   Google Scholar
• R. Leplaideur and D. Yang, SRB measure for higher dimensional singular partially hyperbolic attractors, Ann. Inst. Fourier 67 (2017), pp. 2703–2717.
   Web of Science ®Google Scholar
• R. Metzger and C. Morales, Sectional-hyperbolic systems, Ergodic Theory Dyn. Syst. 28 (2008), pp. 1587–1597.
   Web of Science ®Google Scholar
• R. Metzger and C.A. Morales, Stochastic stability of sectional-anosov flows, preprint (2015). Available at arXiv:1505.01761.
   Google Scholar
• Z. Mi and Y. Cao, Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers. Availalbe at arXiv:2003.04512.
   Google Scholar
• Z. Mi, B. You, and Y. Zang, SRB measures for partially hyperbolic flows with mostly expanding center. Available at arXiv:2007.04559v1.
   Google Scholar
• D. Ruelle, A measure associated with axiom-A attractors, Am. J. Math. 98 (1976), pp. 619–654.
   Web of Science ®Google Scholar
• E. Sataev, Invariant measures for singular hyperbolic attractors, Sbornik: Math. 201(3) (2010), pp. 419–470.
   Web of Science ®Google Scholar
• Y. Sinai, Gibbs measure in ergodic theory, Uspehi Mat. Nauk. 27 (1972), pp. 21–69.
   Google Scholar
• M. Viana and J. Yang, Physical measures and absolute continuity for one-dimensional center direction, Ann. Inst. H. Poincar$\acute{e}$ Anal. Non Lin$\acute{e}$aire 30 (2013), pp. 845–877.
   Web of Science ®Google Scholar
• P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, Berlin, 1982.
   Google Scholar
• J. Yang, Entropy along expanding foliations. Available at arXiv:1601.05504v1.
   Google Scholar
• J. Yang, Geometrical and measure-theoretic structures of maps with mostly expanding center. Available at arXiv:1904.10880v1.
   Google Scholar
• L.-S. Young, What are SRB measures, and which dynamical systems have them?, J. Stat. Phys. 108 (2002), pp. 733–754.
   Web of Science ®Google Scholar