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1996-1997 | 65 | 2 | 171-177
Tytuł artykułu

Hyperbolic homeomorphisms and bishadowing

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Hyperbolic homeomorphisms on compact manifolds are shown to have both inverse shadowing and bishadowing properties with respect to a class of δ-methods which are represented by continuous mappings from the manifold into the space of bi-infinite sequences in the manifold with the product topology. Topologically stable homeomorphisms and expanding mappings are also considered.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
65
Numer
2
Strony
171-177
Opis fizyczny
Daty
wydano
1997
otrzymano
1986-02-08
Twórcy
  • School of Computing and Mathematics, Deakin University, Geelong Campus, Geelong, Victoria 3217, Australia
autor
  • Institute of Mathematics, Polish Academy of Sciences, Cracow Branch, Św. Tomasza 30, 31-027 Kraków, Poland
Bibliografia
  • [1] N. Aoki, Topological Dynamics, in: Topics in General Topology, K. Morita and J. Nagata (eds.), Elsevier, 1989, 625-739.
  • [2] R. Corless and S. Pilyugin, Approximate and real trajectories for generic dynamical systems, J. Math. Anal. Appl. 189 (1995), 409-423.
  • [3] P. Diamond, P. E. Kloeden, V. Kozyakin and A. Pokrovskiĭ, Expansivity of semi-hyperbolic Lipschitz mappings, Bull. Austral. Math. Soc. 51 (1995), 301-308.
  • [4] P. Diamond, P. E. Kloeden, V. Kozyakin and A. Pokrovskiĭ, Computer robustness of semi-hyperbolic mappings, Random Comput. Dynam. 3 (1995), 57-70.
  • [5] P. Diamond, P. E. Kloeden, V. Kozyakin and A. Pokrovskiĭ, Robustness of observed behaviour of semi-hyperbolic dynamical systems, Avtomat. i Telemekh. 11 (1995), to appear (in Russian).
  • [6] P. Diamond, P. E. Kloeden and A. Pokrovskiĭ, Shadowing and approximation in dynamical systems, in: CMA 3rd Miniconference on Analysis, G. Martin and H. B. Thompson (eds.), Proc. Centre Math. Appl. Austral. Nat. Univ. 33, Austral. Nat. Univ., Canberra, 1994, 47-60.
  • [7] R. Ma né, Ergodic Theory and Differentiable Dynamics, Springer, 1987.
  • [8] J. Munkres, Elementary Differential Topology, Princeton Univ. Press, 1963.
  • [9] J. Ombach, Equivalent conditions for hyperbolic coordinates, Topology Appl. 23 (1986), 87-90.
  • [10] J. Ombach, Consequences of the pseudo-orbits tracing property and expansiveness, J. Austral. Math. Soc. Ser. A 43 (1987), 301-313.
  • [11] J. Ombach, Expansive homeomorphisms with the pseudo orbits tracing property, preprint 383, Inst. Math. Polish Acad. Sci., 1987.
  • [12] S. Pilyugin, The space of Dynamical Systems with C⁰-Topology, Lecture Notes in Math. 1571, Springer, 1991.
  • [13] D. Ruelle, Thermodynamic Formalism, Addison-Wesley, 1978.
  • [14] P. Walters, On the pseudo-orbit tracing property and its relationship to stability, in: Lecture Notes in Math. 668, Springer, 1978, 231-244.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv65z2p171bwm
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