Extension of zero-dimensional hyperbolic sets to locally maximal ones

Sbornik Mathematics

Volumn 201, Issue 7, 2010, Pages 935-946

  Anosov, D V ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Hyperbolic set; Locally maximal; Shadowing of pseudotrajectories and their families; Zero dimensional

Indexed keywords

EID: 77958536940     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2010v201n07ABEH004097     Document Type: Article

References (7)

1. V. M. Alekseev, "Symbolic dynamics", Eleventh Mathematical School (Summer School, Kolomyya 1973), Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev 1976, pp. 5-210. (Russian)
2. D. V. Anosov, "On a class of invariant sets of smooth dynamical systems", Proc. 5 Int. Conf. on Non-Linear Oscillations, vol. 2, Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev 1970, pp. 39-45. (Russian)
3. S. Crovisier, "Une remarque sur les ensembles hyperboliques localement maximaux", C.R. Math. Acad. Sci. Paris 334:5 (2001), 401-404.
4. T. Fisher, "Hyperbolic sets that are not locally maximal", Ergodic Theory Dynam. Systems 26:5 (2006), 1491-1509.
5. M. Shub, Stabilité globale des systèmes dynamiques, Astérisque, vol. 56, Soc. Math. France, Paris 1978.
6. A. B. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, Faktorial, Moscow 1999; English transl., Encyclopedia Math. Appl., vol. 54, Cambridge Univ. Press, Cambridge 1995.
7. R. Bowen, Methods of symbolic dynamics, Collection of papers, New in foreign science. Mathematics, vol. 13, Mir, Moscow 1979. (Russian)