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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 6, Pages 1328–1344 (Mi izv909)  

This article is cited in 4 scientific papers (total in 4 papers)

Gibbs measures for one-dimensional attractors of hyperbolic mappingss with singularities

E. A. Sataev


Abstract: The author constructs and studies the properties of a $u$-Gibbs invariant measure for hyperbolic mappings with singularities, for which the unstable subspace is one-dimensional and which satisfy some regularity conditions. These conditions are satisfied by the Lorenz mapping, the Lozi mapping and the Belykh mapping among others. Various properties are proved: the denseness of periodic trajectories, topological transitivity, and convergence of the means.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:3, 567–580

Bibliographic databases:

UDC: 517.938
MSC: Primary 58F11, 58F12, 58F15; Secondary 28D05
Received: 29.03.1991

Citation: E. A. Sataev, “Gibbs measures for one-dimensional attractors of hyperbolic mappingss with singularities”, Izv. RAN. Ser. Mat., 56:6 (1992), 1328–1344; Russian Acad. Sci. Izv. Math., 41:3 (1993), 567–580

Citation in format AMSBIB
\Bibitem{Sat92}
\by E.~A.~Sataev
\paper Gibbs measures for one-dimensional attractors of hyperbolic mappingss with singularities
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 6
\pages 1328--1344
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1208166}
\zmath{https://zbmath.org/?q=an:0802.58039}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..567S}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 3
\pages 567--580
\crossref{https://doi.org/10.1070/IM1993v041n03ABEH002276}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993MV05800008}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Sataev, “Invariant measures for hyperbolic maps with singularities”, Russian Math. Surveys, 47:1 (1992), 191–251  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. E. A. Sataev, “Non-existence of stable trajectories in non-autonomous perturbations of systems of Lorenz type”, Sb. Math., 196:4 (2005), 561–594  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. E. A. Sataev, “Invariant measures for singular hyperbolic attractors”, Sb. Math., 201:3 (2010), 419–470  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. E. A. Sataev, “Stokhasticheskie svoistva singulyarno giperbolicheskikh attraktorov”, Nelineinaya dinam., 6:1 (2010), 187–206  mathnet  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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