General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Izv. RAN. Ser. Mat.:

Personal entry:
Save password
Forgotten password?

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.

Full text: PDF file (4172 kB)
References: PDF file   HTML file

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
\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
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 1
\pages 177--218

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. 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
    13. Nantian Qian, Robert J. Zimmer, “Entropy rigidity for semisimple group actions”, Isr J Math, 99:1 (1997), 55  crossref  mathscinet  zmath  isi
    14. Charles Pugh, Michael Shub, “Stably Ergodic Dynamical Systems and Partial Hyperbolicity”, Journal of Complexity, 13:1 (1997), 125  crossref
    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
    16. Viorel Niţică, Andrei Török, “An open dense set of stably ergodic diffeomorphisms in a neighborhood of a non-ergodic one”, Topology, 40:2 (2001), 259  crossref
    17. Dmitry Dolgopyat, “On mixing properties of compact group extensions of hyperbolic systems”, Isr J Math, 130:1 (2002), 157  crossref  mathscinet  zmath  isi
    18. Augusto Armando, Castro Júnior, “Backward inducing and exponential decay of correlations for partially hyperbolic attractors”, Isr J Math, 130:1 (2002), 29  crossref  mathscinet  zmath  isi
    19. Flavio Abdenur, Christian Bonatti, Lorenzo J Díaz, “Non-wandering sets with non-empty interiors”, Nonlinearity, 17:1 (2004), 175  crossref  elib
    20. Christian Bonatti, Amie Wilkinson, “Transitive partially hyperbolic diffeomorphisms on 3-manifolds”, Topology, 44:3 (2005), 475  crossref
    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
    24. A. Katok, V. Niţică, “Rigidity of higher rank abelian cocycles with values in diffeomorphism groups”, Geom Dedicata, 124:1 (2007), 109  crossref  mathscinet  zmath  isi
    25. Michihiro Hirayama, Yakov Pesin, “Non-absolutely continuous foliations”, Isr J Math, 160:1 (2007), 173  crossref  mathscinet  zmath  isi
    26. F. Rodriguez Hertz, M.A. Rodriguez Hertz, R. Ures, “Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle”, Invent math, 172:2 (2008), 353  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. Luis Barreira, Claudia Valls, “Polynomial growth rates”, Nonlinear Analysis: Theory, Methods & Applications, 71:11 (2009), 5208  crossref
    28. Sylvain Crovisier, “Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems”, Ann of Math, 172:3 (2010), 1641  crossref
    29. Luis Barreira, Claudia Valls, “Lyapunov functions for trichotomies with growth rates☆”, Journal of Differential Equations, 248:1 (2010), 151  crossref
    30. Raúl Ures, María Hertz, Federico Hertz, “Tori with hyperbolic dynamics in 3-manifolds”, JMD, 5:1 (2011), 185  crossref
    31. Andy Hammerlindl, “Dynamics of quasi-isometric foliations”, Nonlinearity, 25:6 (2012), 1585  crossref
    32. ANDY HAMMERLINDL, “Leaf conjugacies on the torus”, Ergod. Th. Dynam. Sys, 2013, 1  crossref
    33. LAN XU, BEIMEI CHEN, “TWO NOTES ABOUT THE ERGODICITY OF PARTIALLY HYPERBOLIC SYSTEMS”, Int. J. Bifurcation Chaos, 23:07 (2013), 1350123  crossref
    34. Yujun Zhu, “Topological quasi-stability of partially hyperbolic diffeomorphisms under random perturbations”, DCDS-A, 34:2 (2013), 869  crossref
    35. A. Hammerlindl, R. Potrie, “Pointwise partial hyperbolicity in three-dimensional nilmanifolds”, Journal of the London Mathematical Society, 2014  crossref
    36. Vyacheslav Z. Grines, Yulia A. Levchenko, Vladislav S. Medvedev, Olga V. Pochinka, “On the Dynamical Coherence of Structurally Stable 3-diffeomorphisms”, Regul. Chaotic Dyn., 19:4 (2014), 506–512  mathnet  crossref  mathscinet  zmath
    37. HUYI HU, YUNHUA ZHOU, YUJUN ZHU, “Quasi-shadowing for partially hyperbolic diffeomorphisms”, Ergod. Th. Dynam. Sys, 2014, 1  crossref
    38. WEISHENG WU, “Schmidt games and non-dense forward orbits of certain partially hyperbolic systems”, Ergod. Th. Dynam. Sys, 2015, 1  crossref
    39. Lin Wang, Yujun Zhu, “Center specification property and entropy for partially hyperbolic diffeomorphisms”, DCDS-A, 36:1 (2015), 469  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:599
    Full text:193
    First page:1

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019