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This article is cited in 6 scientific papers (total in 6 papers)
Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products
L. J. Díaza, K. Gelfertb, M. Ramsc a Departamento de Matemá'tica PUC-Rio, Marquês de São Vicente 225, Gávea, Rio de Janeiro 22451-900, Brazil
b Instituto de Matemática Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Cidade
Universitária — Ilha do Fundão, Rio de Janeiro 21945-909, Brazil
c Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland
Abstract:
We review some ergodic and topological aspects of robustly transitive partially hyperbolic diffeomorphisms with one-dimensional center direction. We also discuss step skew-product maps whose fiber maps are defined on the circle which model such dynamics. These dynamics are genuinely nonhyperbolic and exhibit simultaneously ergodic measures with positive, negative, and zero exponents as well as intermingled horseshoes having different types of hyperbolicity. We discuss some recent advances concerning the topology of the space of invariant measures and properties of the spectrum of Lyapunov exponents.
Received: March 15, 2017
Citation:
L. J. Díaz, K. Gelfert, M. Rams, “Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Trudy Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 113–132; Proc. Steklov Inst. Math., 297 (2017), 98–115
Linking options:
https://www.mathnet.ru/eng/tm3841https://doi.org/10.1134/S0371968517020066 https://www.mathnet.ru/eng/tm/v297/p113
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Abstract page: | 230 | Full-text PDF : | 41 | References: | 37 | First page: | 8 |
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