Stable ergodicity of skew products
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 6, pp. 859-889.
@article{ASENS_1999_4_32_6_859_0,
     author = {Burns, Keith and Wilkinson, Amie},
     title = {Stable ergodicity of skew products},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {859--889},
     publisher = {Elsevier},
     volume = {Ser. 4, 32},
     number = {6},
     year = {1999},
     doi = {10.1016/s0012-9593(00)87721-6},
     mrnumber = {2000g:37030},
     zbl = {0942.37015},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/s0012-9593(00)87721-6/}
}
TY  - JOUR
AU  - Burns, Keith
AU  - Wilkinson, Amie
TI  - Stable ergodicity of skew products
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1999
SP  - 859
EP  - 889
VL  - 32
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/s0012-9593(00)87721-6/
DO  - 10.1016/s0012-9593(00)87721-6
LA  - en
ID  - ASENS_1999_4_32_6_859_0
ER  - 
%0 Journal Article
%A Burns, Keith
%A Wilkinson, Amie
%T Stable ergodicity of skew products
%J Annales scientifiques de l'École Normale Supérieure
%D 1999
%P 859-889
%V 32
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/s0012-9593(00)87721-6/
%R 10.1016/s0012-9593(00)87721-6
%G en
%F ASENS_1999_4_32_6_859_0
Burns, Keith; Wilkinson, Amie. Stable ergodicity of skew products. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 6, pp. 859-889. doi : 10.1016/s0012-9593(00)87721-6. https://www.numdam.org/articles/10.1016/s0012-9593(00)87721-6/

[AKS] R. Adler, B. Kitchens and M. Shub, Stably ergodic skew products, Discrete and Continuous Dynamical Systems, Vol. 2, 1996, pp. 349-350. | MR | Zbl

[B1] M. Brin, Topological transitivity of one class of dynamical systems and flows of frames on manifolds of negative curvature, Func. Anal. Appl., Vol. 9, 1975, no. 1, pp. 9-19. | MR | Zbl

[B2] M. Brin, The topology of group extensions of C systems, Mat. Zametki, Vol. 18, 1975, no. 3, pp. 453-465. | MR | Zbl

[BP] M. Brin and Ja. Pesin, Partially hyperbolic dynamical systems, Math. USSR Izvestija, Vol. 8, 1974, no. 1, pp. 177-218. | Zbl

[BPW] K. Burns, C. Pugh and A. Wilkinson, Stable ergodicity and Anosov flows, to appear in Topology. | Zbl

[CE] J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North Holland/American Elsevier, 1975. | MR | Zbl

[FP] M. Field and W. Parry, Stable ergodicity of skew extensions by compact Lie groups, Topology, Vol. 38, 1999, No 1, pp. 167-187. | MR | Zbl

[GPS] M. Grayson, C. Pugh and M. Shub, Stably ergodic diffeomorphisms, Ann. Math., Vol. 140, 1994, pp. 295-329. | MR | Zbl

[H] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978. | MR | Zbl

[HPS] M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, 1977. | MR | Zbl

[Hu] S.-T. Hu, Homotopy Theory, Academic Press, 1959. | MR | Zbl

[Hum] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer Verlag, 1972. | MR | Zbl

[J] J.-L. Journé, A regularity lemma for functions of several variables, Rev. Mat. Iberoamericana, Vol. 4, 1988, no. 2, pp. 187-193. | MR | Zbl

[KK] A. Katok and A. Kononenko, Cocycles' stability for partially hyperbolic systems, Math. Res. Lett., Vol. 3, 1996, no. 2, pp. 191-210. | MR | Zbl

[Ma1] A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., Vol. 96, 1974, pp. 422-429. | MR | Zbl

[Ma2] A. Manning, Anosov diffeomorphisms on nilmanifolds, Proc. Amer. Math. Soc., Vol. 38, 1973, pp. 423-426. | MR | Zbl

[Mi] J. Milnor, Morse Theory, Princeton University Press, 1969.

[N] K. Nomizu, Lie Groups and Differential Geometry, Mathematical Society of Japan, 1956. | MR | Zbl

[P] W. Parry, Entropy and Generators in Ergodic Theory, W. A. Benjamin, Inc. 1969. | MR | Zbl

[PP] W. Parry and M. Pollicott, Stability of mixing for toral extensions of hyperbolic systems, Tr. Mat. Inst. Steklova, Vol. 216, 1997, Din. Sist. i Smezhnye Vopr., pp. 354-363. | MR | Zbl

[PS1] C. Pugh and M. Shub, Stably ergodic dynamical systems and partial hyperbolicity, J. of Complexity, Vol. 13, 1997, pp. 125-179. | MR | Zbl

[PS2] C. Pugh and M. Shub, Stable ergodicity and julienne quasiconformality, September, 1997 preprint.

[R] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, J. Analyse Math., Vol. 34, 1978, pp. 36-60. | MR | Zbl

[Wa] C. Walkden, Stable ergodic properties of cocycles over hyperbolic attractors, 1997 preprint.

[Wi] A. Wilkinson, Stable ergodicity of the time one map of a geodesic flow, Ergod. Th. and Dynam. Syst., Vol. 18, 1998, no. 6, pp. 1545-1588. | MR | Zbl

[Y] H. Yamabe, On an arcwise connected subgroup of a Lie group, Osaka Math. J., Vol. 2, 1950, pp. 13-14. | MR | Zbl

  • Chakraborty, Sankhadip; Viana, Marcelo Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems, Journal of Dynamics and Differential Equations (2024) | DOI:10.1007/s10884-023-10343-6
  • Dong, Changguang On ergodic properties of time changes of partially hyperbolic homogeneous flows, Journal of Modern Dynamics, Volume 19 (2023) no. 0, p. 541 | DOI:10.3934/jmd.2023015
  • Damjanović, Danijela; Wilkinson, Amie; Xu, Disheng Pathology and asymmetry: Centralizer rigidity for partially hyperbolic diffeomorphisms, Duke Mathematical Journal, Volume 170 (2021) no. 17 | DOI:10.1215/00127094-2021-0053
  • Carrasco, Pablo D. Random Products of Standard Maps, Communications in Mathematical Physics, Volume 377 (2020) no. 2, p. 773 | DOI:10.1007/s00220-020-03765-6
  • Rodriguez Hertz, Jana; Ures, Raúl On the Three-Legged Accessibility Property, New Trends in One-Dimensional Dynamics, Volume 285 (2019), p. 239 | DOI:10.1007/978-3-030-16833-9_13
  • Chen, Jianyu; Hu, Huyi The spectral gap for transfer operators of torus extensions over expanding maps, Nonlinearity, Volume 32 (2019) no. 1, p. 356 | DOI:10.1088/1361-6544/aaea87
  • Anastassiou, Stavros; Bountis, Anastasios; Bäcker, Arnd Recent Results on the Dynamics of Higher-dimensional Hénon Maps, Regular and Chaotic Dynamics, Volume 23 (2018) no. 2, p. 161 | DOI:10.1134/s156035471802003x
  • Dolgopyat, Dmitry The work of Federico Rodriguez Hertz on ergodicity of dynamical systems, Journal of Modern Dynamics, Volume 10 (2016) no. 02, p. 175 | DOI:10.3934/jmd.2016.10.175
  • Nitica, Viorel; Török, Andrei Open and Dense Topological Transitivity of Extensions by Non-Compact Fiber of Hyperbolic Systems: A Review, Axioms, Volume 4 (2015) no. 1, p. 84 | DOI:10.3390/axioms4010084
  • CARRASCO, PABLO D. Compact dynamical foliations, Ergodic Theory and Dynamical Systems, Volume 35 (2015) no. 8, p. 2474 | DOI:10.1017/etds.2014.42
  • Tahzibi, Ali; Gogolev, Andrey Center Lyapunov exponents in partially hyperbolic dynamics, Journal of Modern Dynamics, Volume 8 (2015) no. 3/4, p. 549 | DOI:10.3934/jmd.2014.8.549
  • Viana, Marcelo; Yang, Jiagang Physical measures and absolute continuity for one-dimensional center direction, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 30 (2013) no. 5, p. 845 | DOI:10.1016/j.anihpc.2012.11.002
  • RUGGIERO, RAFAEL OSWALDO The accessibility property of expansive geodesic flows without conjugate points, Ergodic Theory and Dynamical Systems, Volume 28 (2008) no. 1, p. 229 | DOI:10.1017/s0143385707000399
  • Rodriguez Hertz, F.; Rodriguez Hertz, M.A.; Ures, R. Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle, Inventiones mathematicae, Volume 172 (2008) no. 2, p. 353 | DOI:10.1007/s00222-007-0100-z
  • Hasselblatt, Boris; Pesin, Yakov Partially Hyperbolic Dynamical Systems, Volume 1 (2006), p. 1 | DOI:10.1016/s1874-575x(06)80026-3
  • Bonatti, Christian; Wilkinson, Amie Transitive partially hyperbolic diffeomorphisms on 3-manifolds, Topology, Volume 44 (2005) no. 3, p. 475 | DOI:10.1016/j.top.2004.10.009
  • Field, Michael Persistent Ergodicity and Stably Ergodic SRB Attractors in Equivariant Dynamics, Bifurcation, Symmetry and Patterns (2003), p. 75 | DOI:10.1007/978-3-0348-7982-8_4
  • Pugh, Charles; Shub, Michael; Starkov, an appendix by Alexander Stable ergodicity, Bulletin of the American Mathematical Society, Volume 41 (2003) no. 1, p. 1 | DOI:10.1090/s0273-0979-03-00998-4
  • McLachlan, R.I.; Perlmutter, M.; Quispel, G.R.W. Lie group foliations: dynamical systems and integrators, Future Generation Computer Systems, Volume 19 (2003) no. 7, p. 1207 | DOI:10.1016/s0167-739x(03)00046-3
  • Ruelle, David Perturbation theory for Lyapunov exponents of a toral map: Extension of a result of Shub and Wilkinson, Israel Journal of Mathematics, Volume 134 (2003) no. 1, p. 345 | DOI:10.1007/bf02787412
  • Dolgopyat, Dmitry On mixing properties of compact group extensions of hyperbolic systems, Israel Journal of Mathematics, Volume 130 (2002) no. 1, p. 157 | DOI:10.1007/bf02764076
  • NiţicĂ, Viorel A note about topologically transitive cylindrical cascades, Israel Journal of Mathematics, Volume 126 (2001) no. 1, p. 141 | DOI:10.1007/bf02784152
  • McLachlan, Robert; Perlmutter, Matthew Conformal Hamiltonian systems, Journal of Geometry and Physics, Volume 39 (2001) no. 4, p. 276 | DOI:10.1016/s0393-0440(01)00020-1
  • Nicol, Matthew; Melbourne, Ian; Ashwin, Peter Euclidean extensions of dynamical systems, Nonlinearity, Volume 14 (2001) no. 2, p. 275 | DOI:10.1088/0951-7715/14/2/306

Cité par 24 documents. Sources : Crossref