ArticleOriginal scientific text

Title

The simplest shadowing

Authors 1

Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

Two different and easy proofs are presented that a hyperbolic linear homeomorphism of a Banach space admits the shadowing.

Keywords

hyperbolic, shadowing, pseudo-orbit, contraction, expansive

Bibliography

  1. R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math. 470, Springer, 1975.
  2. M. C. Irwin, Smooth Dynamical Systems, Academic Press, 1980.
  3. S. Kakubari, A note on a linear homeomorphism on n with the pseudo-orbit tracing property, Sci. Rep. Niigata Univ. Ser. A 23 (1987), 35-37.
  4. A. Katok, Local properties of hyperbolic sets (in Russian), appendix to the Russian edition of: Z. Nitecki, Differentiable Dynamics, Mir, Moscow, 1975.
  5. K. Meyer and G. Sell, An analytic proof of the Shadowing Lemma, Funkc. Ekvac. 30 (1987), 127-133.
  6. A. Morimoto, Some stabilities of group automorphisms, in: Manifolds and Lie Groups, Progr. Math. 14, Birkhäuser, 1981, 283-299.
  7. J. Ombach, The Shadowing Lemma in the linear case, Univ. Iagell. Acta Math., to appear.
  8. M. Shub, Global Stability of Dynamical Systems, Springer, 1987.
Pages:
253-258
Main language of publication
English
Received
1992-03-16
Published
1993
Exact and natural sciences