Hyperbolic homeomorphisms and bishadowing

P. E. Kloeden; J. Ombach

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 2, page 171-177
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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P. E. Kloeden, and J. Ombach. "Hyperbolic homeomorphisms and bishadowing." Annales Polonici Mathematici 65.2 (1997): 171-177. <http://eudml.org/doc/269979>.

@article{P1997,
abstract = {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.},
author = {P. E. Kloeden, J. Ombach},
journal = {Annales Polonici Mathematici},
keywords = {pseudo-orbit; hyperbolic; shadowing; hyperbolic homeomorphism; topologically stable homeomorphism; expanding map},
language = {eng},
number = {2},
pages = {171-177},
title = {Hyperbolic homeomorphisms and bishadowing},
url = {http://eudml.org/doc/269979},
volume = {65},
year = {1997},
}

TY - JOUR
AU - P. E. Kloeden
AU - J. Ombach
TI - Hyperbolic homeomorphisms and bishadowing
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 2
SP - 171
EP - 177
AB - 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.
LA - eng
KW - pseudo-orbit; hyperbolic; shadowing; hyperbolic homeomorphism; topologically stable homeomorphism; expanding map
UR - http://eudml.org/doc/269979
ER -

References

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  2. [2] R. Corless and S. Pilyugin, Approximate and real trajectories for generic dynamical systems, J. Math. Anal. Appl. 189 (1995), 409-423. Zbl0821.58036
  3. [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. Zbl0826.58028
  4. [4] P. Diamond, P. E. Kloeden, V. Kozyakin and A. Pokrovskiĭ, Computer robustness of semi-hyperbolic mappings, Random Comput. Dynam. 3 (1995), 57-70. Zbl0849.58051
  5. [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). Zbl0849.58051
  6. [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. [7] R. Ma né, Ergodic Theory and Differentiable Dynamics, Springer, 1987. 
  8. [8] J. Munkres, Elementary Differential Topology, Princeton Univ. Press, 1963. 
  9. [9] J. Ombach, Equivalent conditions for hyperbolic coordinates, Topology Appl. 23 (1986), 87-90. Zbl0597.58023
  10. [10] J. Ombach, Consequences of the pseudo-orbits tracing property and expansiveness, J. Austral. Math. Soc. Ser. A 43 (1987), 301-313. Zbl0653.58030
  11. [11] J. Ombach, Expansive homeomorphisms with the pseudo orbits tracing property, preprint 383, Inst. Math. Polish Acad. Sci., 1987. 
  12. [12] S. Pilyugin, The space of Dynamical Systems with C⁰-Topology, Lecture Notes in Math. 1571, Springer, 1991. 
  13. [13] D. Ruelle, Thermodynamic Formalism, Addison-Wesley, 1978. 
  14. [14] P. Walters, On the pseudo-orbit tracing property and its relationship to stability, in: Lecture Notes in Math. 668, Springer, 1978, 231-244. 

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