Une remarque sur les ensembles hyperboliques localement maximaux
Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 401-404.

Nous montrons sur un exemple qu'il existe des ensembles hyperboliques qui ne sont contenus dans aucun ensemble hyperbolique localement maximal.

On an example we show that there exist some hyperbolic sets which are not contained in any locally maximal hyperbolic set.

Reçu le :
Publié le :
DOI : 10.1016/S1631-073X(02)02274-4
Crovisier, Sylvain 1

1 Département de mathématiques, Université Paris-Sud, bâtiment 425, 91405 Orsay cedex, France
@article{CRMATH_2002__334_5_401_0,
     author = {Crovisier, Sylvain},
     title = {Une remarque sur les ensembles hyperboliques localement maximaux},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {401--404},
     publisher = {Elsevier},
     volume = {334},
     number = {5},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02274-4},
     language = {fr},
     url = {https://www.numdam.org/articles/10.1016/S1631-073X(02)02274-4/}
}
TY  - JOUR
AU  - Crovisier, Sylvain
TI  - Une remarque sur les ensembles hyperboliques localement maximaux
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 401
EP  - 404
VL  - 334
IS  - 5
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/S1631-073X(02)02274-4/
DO  - 10.1016/S1631-073X(02)02274-4
LA  - fr
ID  - CRMATH_2002__334_5_401_0
ER  - 
%0 Journal Article
%A Crovisier, Sylvain
%T Une remarque sur les ensembles hyperboliques localement maximaux
%J Comptes Rendus. Mathématique
%D 2002
%P 401-404
%V 334
%N 5
%I Elsevier
%U https://www.numdam.org/articles/10.1016/S1631-073X(02)02274-4/
%R 10.1016/S1631-073X(02)02274-4
%G fr
%F CRMATH_2002__334_5_401_0
Crovisier, Sylvain. Une remarque sur les ensembles hyperboliques localement maximaux. Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 401-404. doi : 10.1016/S1631-073X(02)02274-4. https://www.numdam.org/articles/10.1016/S1631-073X(02)02274-4/

[1] Bonatti, C.; Díaz, L. Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math., Volume 143 (1995), pp. 357-396

[2] Hasselblatt, B.; Katok, A. Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995

[3] Hirsch, M.; Pugh, C.; Shub, M. Invariant Manifolds, Lecture Notes in Math., 583, Springer-Verlag, 1977

[4] Shub, M. Topologically Transitive Diffeomorphisms on 𝕋4, Lecture Notes in Math., 206, Springer-Verlag, 1971

[5] Shub, M. Stabilité Globale des Systèmes Dynamiques, Astérisque, 56, Sociéte Mathématique de France, 1978

[6] Smale, S. Differentiable dynamical systems, Bull. Amer. Math. Soc., Volume 73 (1967), pp. 747-817

  • da Luz, Adriana Hyperbolic sets that are not contained in a locally maximal one, Discrete Continuous Dynamical Systems - A, Volume 37 (2017) no. 9, p. 4923 | DOI:10.3934/dcds.2017166
  • Wang, Lei; Yang, Xiao-Song Topological horseshoe and its uniform hyperbolicity in the HP model, Journal of Mathematical Biology, Volume 75 (2017) no. 1, p. 129 | DOI:10.1007/s00285-016-1076-3
  • Wang, Lei; Yang, Xiao-Song Uniform hyperbolicity of locally maximal chaotic invariant sets in a system with only one stable equilibrium**This work was supported by the National Natural Science Foundation of China (11472111) and the Key Construction Disciplines Foundation of Hefei University (2014xk08)., IFAC-PapersOnLine, Volume 48 (2015) no. 18, p. 205 | DOI:10.1016/j.ifacol.2015.11.037
  • Burns, Keith; Gelfert, Katrin Lyapunov spectrum for geodesic flows of rank 1 surfaces, Discrete Continuous Dynamical Systems - A, Volume 34 (2014) no. 5, p. 1841 | DOI:10.3934/dcds.2014.34.1841
  • Anosov, D. V. On Trajectories Entirely Situated Near a Hyperbolic Set, Journal of Mathematical Sciences, Volume 201 (2014) no. 5, p. 553 | DOI:10.1007/s10958-014-2011-z
  • LIZANA, CRISTINA; PUJALS, ENRIQUE Robust transitivity for endomorphisms, Ergodic Theory and Dynamical Systems, Volume 33 (2013) no. 4, p. 1082 | DOI:10.1017/s0143385712000247
  • Anosov, D. V. Local maximality of hyperbolic sets, Proceedings of the Steklov Institute of Mathematics, Volume 273 (2011) no. 1, p. 23 | DOI:10.1134/s008154381104002x
  • Anosov, D. V. Intrinsic Character of One Property of Hyperbolic Sets, Journal of Dynamical and Control Systems, Volume 16 (2010) no. 4, p. 485 | DOI:10.1007/s10883-010-9103-y
  • Anosov, D. V. On certain hyperbolic sets, Mathematical Notes, Volume 87 (2010) no. 5-6, p. 608 | DOI:10.1134/s0001434610050020
  • Anosov, Dmitry V Extension of zero-dimensional hyperbolic sets to locally maximal ones, Sbornik: Mathematics, Volume 201 (2010) no. 7, p. 935 | DOI:10.1070/sm2010v201n07abeh004097
  • Аносов, Дмитрий Викторович; Anosov, Dmitry Victorovich О некоторых гиперболических множествах, Математические заметки, Volume 87 (2010) no. 5, p. 650 | DOI:10.4213/mzm8715
  • Аносов, Дмитрий Викторович; Anosov, Dmitry Victorovich Расширение нульмерных гиперболических множеств до локально максимальных, Математический сборник, Volume 201 (2010) no. 7, p. 3 | DOI:10.4213/sm7647

Cité par 12 documents. Sources : Crossref