Topological pressure for conservative C¹-diffeomorphisms with no dominated splitting

References

• F. Abdenur, C. Bonatti, and S. Crovisier, Nonuniform hyperbolicity for C1-generic diffeomorphisms, Isr. J. Math. 183(1) (2011), pp. 1–60.
   Web of Science ®Google Scholar
• A. Arbieto and L Prudente, Uniqueness of equilibrium states for some partially hyperbolic horseshoes, Discrete Contin. Dyn. Syst. 32(1) (2012), pp. 27–40.
   Web of Science ®Google Scholar
• M.C. Arnaud, C. Bonatti, and S. Crovisier, Dynamiques symplectiques génériques, Ergod. Theory Dyn. Syst. 25(5) (2005), pp. 1401–1436.
   Google Scholar
• J. Bochi, Genericity of zero Lyapunov exponents, Ergod. Theory Dyn. Syst. 22(6) (2002), pp. 1667–1696.
   Web of Science ®Google Scholar
• C. Bonatti and S. Crovisier, Recurrence and genericity, C. R. Math. 336(10) (2003), pp. 839–844.
   Web of Science ®Google Scholar
• R. Bowen, Entropy-Expansive maps, Trans. Am. Math. Soc. 164 (1972), pp. 323–331.
   Web of Science ®Google Scholar
• R. Bowen, D. Ruelle, and J.R. Chazottes, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Springer Berlin Heidelberg, 2008.
   Google Scholar
• J. Buzzi and T. Fisher, Entropic stability beyond partial hyperbolicity, J. Mod. Dyn. 7(4) (2013), pp. 527–552.
   Web of Science ®Google Scholar
• J. Buzzi, S. Crovisier, and T. Fisher, Local perturbations of conservative C1 diffeomorphisms, Nonlinearity30(9) (2017), pp. 3613–3636.
   Web of Science ®Google Scholar
• J. Buzzi, S. Crovisier, and T. Fisher, The entropy of C1-diffeomorphisms without a dominated splitting, Trans. Amer. Math. Soc. 370(9) (2018), pp. 6685–6734.
   Web of Science ®Google Scholar
• W. Cowieson and L-S. Young, SRB measures as zero-noise limits, Ergod. Theory Dyn. Syst. 25(4) (2005), pp. 1115–1138.
   Web of Science ®Google Scholar
• J. Crisostomo and A. Tahzibi, Equilibrium states for partially hyperbolic diffeomorphisms with hyperbolic linear part, Nonlinearity 32(2) (2019), pp. 584–602.
   Web of Science ®Google Scholar
• L.J. Díaz and K. Gelfert, Porcupine-like horseshoes: transitivity, Lyapunov spectrum, and phase transitions, Fundam. Math. 216 (2010), pp. 55–100.
   Web of Science ®Google Scholar
• L.J. Díaz, K. Gelfert, and M. Rams, Rich phase transitions in step skew products, Nonlinearity24(12) (2011), pp. 3391–3412.
   Web of Science ®Google Scholar
• L.J. Díaz, K. Gelfert, and K. Rams, Abundant rich phase transitions in step-skew products, Nonlinearity 27(9) (2014), pp. 2255–2280.
   Web of Science ®Google Scholar
• J. Franks, Necessary conditions for stability of diffeomorphisms, Trans. Am. Math. Soc. 158(2) (1971), pp. 301–308.
   Web of Science ®Google Scholar
• I. Inoquio-Renteria and J. Rivera-Letelier, A characterization of hyperbolic potentials of rational maps, Bull. Braz. Math. Soc. New Ser. 43(1) (2012), pp. 99–127.
   Google Scholar
• A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. Math. Inst. Hautes Etudes Sci. 51(1) (1980), pp. 137–173.
   Google Scholar
• R. Leplaideur, K. Oliveira, and I. Rios, Equilibrium states for partially hyperbolic horseshoes, Ergod. Theory Dyn. Syst. 31(1) (2011), pp. 179–195.
   Web of Science ®Google Scholar
• R. Mañé, An ergodic closing lemma, Ann. Math. 116(3) (1982), pp. 503–540.
   Web of Science ®Google Scholar
• S.E. Newhouse, Quasi-elliptic periodic points in conservative dynamical systems, Am. J. Math. 99(5) (1977), pp. 1061–1087.
   Web of Science ®Google Scholar
• S.E. Newhouse, Continuity properties of entropy, Ann. Math. 129(1) (1989), pp. 215–235.
   Google Scholar
• V.I. Osedelec, A multiplicative ergodic theorem: Lyapunov characteristic exponents for dynamical systems, Trans. Mosc. Math. Soc. 19 (1968), pp. 197–231.
   Google Scholar
• V. Ramos and J. Siqueira, On equilibrium states for partially hyperbolic horseshoes: uniqueness and statistical properties, Bull. Braz. Math. Soc. New Ser. 48(3) (2017), pp. 347–375.
   Google Scholar
• V. Ramos and M. Viana, Equilibrium states for hyperbolic potentials, Nonlinearity 30(2) (2017), pp. 825–847.
   Web of Science ®Google Scholar
• I. Rios and J. Siqueira, On equilibrium states for partially hyperbolic horseshoes, Ergod. Theory Dyn. Syst. 38(1) (2018), pp. 301–335.
   Google Scholar
• V.A. Rohlin, Lectures on the entropy theory of transformations with invariant measure, Usp. Mat. Nauk. 22(5(137)) (1967), pp. 3–56.
   Google Scholar
• D. Ruelle, A measure associated with Axiom-A attractors, Am. J. Math. 98(3) (1976), pp. 619–654.
   Web of Science ®Google Scholar
• D. Ruelle, An inequality for the entropy of differentiable maps, Bull. Braz. Math. Soc. 9(1) (1978), pp. 83–87.
   Google Scholar
• P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Springer, New York, 2000.
   Google Scholar