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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 1, Pages 170–212 (Mi izv1897)  

This article is cited in 39 scientific papers (total in 39 papers)

Partially hyperbolic dynamical systems

M. I. Brin, Ya. B. Pesin


Abstract: Smooth dynamical systems having contracting and expanding invariant foliations (of not necessarily complementary dimensions) are investigated. Ergodicity and the $K$-property are established for such dynamical systems under additional assumptions.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:1, 177–218

Bibliographic databases:

UDC: 517.9
MSC: 58F15, 28A65
Received: 29.05.1973

Citation: M. I. Brin, Ya. B. Pesin, “Partially hyperbolic dynamical systems”, Izv. Akad. Nauk SSSR Ser. Mat., 38:1 (1974), 170–212; Math. USSR-Izv., 8:1 (1974), 177–218

Citation in format AMSBIB
\Bibitem{BriPes74}
\by M.~I.~Brin, Ya.~B.~Pesin
\paper Partially hyperbolic dynamical systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 1
\pages 170--212
\mathnet{http://mi.mathnet.ru/izv1897}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=343316}
\zmath{https://zbmath.org/?q=an:0304.58017}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 1
\pages 177--218
\crossref{https://doi.org/10.1070/IM1974v008n01ABEH002101}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. I. Brin, “Topological transitivity of one class of dynamic systems and flows of frames on manifolds of negative curvature”, Funct. Anal. Appl., 9:1 (1975), 8–16  mathnet  crossref  mathscinet  zmath
    2. Ya. B. Pesin, “Families of invariant manifolds corresponding to nonzero characteristic exponents”, Math. USSR-Izv., 10:6 (1976), 1261–1305  mathnet  crossref  mathscinet  zmath
    3. Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory”, Russian Math. Surveys, 32:4 (1977), 55–114  mathnet  crossref  mathscinet  zmath
    4. A. B. Katok, “Monotone equivalence in ergodic theory”, Math. USSR-Izv., 11:1 (1977), 99–146  mathnet  crossref  mathscinet  zmath  isi
    5. Ya. G. Sinai, “Ergodic properties of the Lorentz gas”, Funct. Anal. Appl., 13:3 (1979), 192–202  mathnet  crossref  mathscinet  zmath
    6. A. Katok, “Lyapunov exponents, entropy and periodic orbits for diffeomorphisms”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 51:1 (1980), 137  crossref  mathscinet  zmath
    7. Ya. B. Pesin, “Geodesic flows with hyperbolic behaviour of the trajectories and objects connected with them”, Russian Math. Surveys, 36:4 (1981), 1–59  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. A. B. Antonevich, A. V. Lebedev, “On spectral properties of operators with a shift”, Math. USSR-Izv., 23:2 (1984), 201–224  mathnet  crossref  mathscinet  zmath
    9. Ya. G. Sinai, N. I. Chernov, “Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls”, Russian Math. Surveys, 42:3 (1987), 181–207  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. L. D. Pustyl'nikov, “New mechanism of particle acceleration and relativistic analog of the Fermi–Ulam model”, Theoret. and Math. Phys., 77:1 (1988), 1110–1115  mathnet  crossref  mathscinet  isi
    11. D. C. Lin, “Characterization of low-energy mode vibrations in chaos using entropy balance versus the amplitude-based Karhunen-Loéve expansion”, Phys Rev E, 52:3 (1995), 2322  crossref  adsnasa  isi
    12. L. D. Pustyl'nikov, “Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism”, Russian Math. Surveys, 50:1 (1995), 145–189  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    15. M. Giona, A. Adrover, “Invariant geometric properties of a class of 3D chaotic flows”, Physica D: Nonlinear Phenomena, 140:1-2 (2000), 50  crossref
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    19. Flavio Abdenur, Christian Bonatti, Lorenzo J Díaz, “Non-wandering sets with non-empty interiors”, Nonlinearity, 17:1 (2004), 175  crossref  elib
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    21. D J Albers, J C Sprott, “Structural stability and hyperbolicity violation in high-dimensional dynamical systems”, Nonlinearity, 19:8 (2006), 1801  crossref  mathscinet  zmath  isi  elib
    22. A. S. Gorodetski, “The regularity of central leaves of partially hyperbolic sets and its applications”, Izv. Math., 70:6 (2006), 1093–1116  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    23. S. Bautista, C. A. Morales, “Existence of periodic orbits for singular-hyperbolic sets”, Mosc. Math. J., 6:2 (2006), 265–297  mathnet  mathscinet  zmath
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    25. Michihiro Hirayama, Yakov Pesin, “Non-absolutely continuous foliations”, Isr J Math, 160:1 (2007), 173  crossref  mathscinet  zmath  isi
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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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