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.
Publié le :
@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] Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math., Volume 143 (1995), pp. 357-396
[2] Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995
[3] Invariant Manifolds, Lecture Notes in Math., 583, Springer-Verlag, 1977
[4] Topologically Transitive Diffeomorphisms on
[5] Stabilité Globale des Systèmes Dynamiques, Astérisque, 56, Sociéte Mathématique de France, 1978
[6] Differentiable dynamical systems, Bull. Amer. Math. Soc., Volume 73 (1967), pp. 747-817
- 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
- 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
- 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
- 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
- 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
- Robust transitivity for endomorphisms, Ergodic Theory and Dynamical Systems, Volume 33 (2013) no. 4, p. 1082 | DOI:10.1017/s0143385712000247
- Local maximality of hyperbolic sets, Proceedings of the Steklov Institute of Mathematics, Volume 273 (2011) no. 1, p. 23 | DOI:10.1134/s008154381104002x
- 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
- On certain hyperbolic sets, Mathematical Notes, Volume 87 (2010) no. 5-6, p. 608 | DOI:10.1134/s0001434610050020
- Extension of zero-dimensional hyperbolic sets to locally maximal ones, Sbornik: Mathematics, Volume 201 (2010) no. 7, p. 935 | DOI:10.1070/sm2010v201n07abeh004097
- О некоторых гиперболических множествах, Математические заметки, Volume 87 (2010) no. 5, p. 650 | DOI:10.4213/mzm8715
- 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