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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 297, Pages 113–132
DOI: https://doi.org/10.1134/S0371968517020066 (Mi tm3841) 		 
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
Full-text PDF (333 kB) Citations (6)
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DOI: https://doi.org/10.1134/S0371968517020066
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.
Funding agency Grant number
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro CNE
National Council for Scientific and Technological Development (CNPq)
National Science Centre (Narodowe Centrum Nauki) 2014/13/B/ST1/01033
European Union's Seventh Framework Programme FP7-PEOPLE-2012-IRSES 318999 BREUDS
The research was supported in part by CNE-FAPERJ and CNPq grants, Brazil (LD and KG), National Science Centre grant 2014/13/B/ST1/01033, Poland (MR), and EU Marie-Curie IRSES “Brazilian–European partnership in Dynamical Systems” (FP7-PEOPLE-2012-IRSES 318999 BREUDS).
Received: March 15, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 297, Pages 98–115
DOI: https://doi.org/10.1134/S008154381704006X
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: 37D25, 37D35, 37D30, 28D20, 28D99
Language: Russian
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
Citation in format AMSBIB
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\paper Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products
\inbook Order and chaos in dynamical systems
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 297
\pages 113--132
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968517020066}
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  • https://www.mathnet.ru/eng/tm3841
  • https://doi.org/10.1134/S0371968517020066
  • https://www.mathnet.ru/eng/tm/v297/p113
    • This publication is cited in the following 6 articles:
    1. L. J. Díaz, K. Gelfert, M. Rams, “Mingled hyperbolicities: Ergodic properties and bifurcation phenomena (an approach using concavity)”, Discrete and Continuous Dynamical Systems, 42:11 (2022), 5309  crossref
    2. G. S. Osipenko, “Encodings of trajectories and invariant measures”, Sb. Math., 211:7 (2020), 1041–1064  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. L. J. Diaz, K. Gelfert, B. Santiago, “Weak and entropy approximation of nonhyperbolic measures: a geometrical approach”, Math. Proc. Camb. Philos. Soc., 169:3 (2020), 507–545  crossref  mathscinet  isi  scopus
    4. L. J. Diaz, K. Gelfert, M. Rams, “Entropy spectrum of lyapunov exponents for nonhyperbolic step skew-products and elliptic cocycles”, Commun. Math. Phys., 367:2 (2019), 351–416  crossref  mathscinet  zmath  isi  scopus
    5. Oliveira E.R., “On the Connection Between a Skew Product Ifs and the Ergodic Optimization For a Finite Family of Potentials”, Dynam. Syst., 34:4 (2019), 685–709  crossref  mathscinet  isi  scopus
    6. L. J. Diaz, K. Gelfert, T. Marcarini, M. Rams, “The structure of the space of ergodic measures of transitive partially hyperbolic sets”, Mon.heft. Math., 190:3 (2019), 441–479  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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