The simplest shadowing

Jerzy Ombach

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 3, page 253-258
  • ISSN: 0066-2216

Abstract

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

How to cite

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Jerzy Ombach. "The simplest shadowing." Annales Polonici Mathematici 58.3 (1993): 253-258. <http://eudml.org/doc/262250>.

@article{JerzyOmbach1993,
abstract = {Two different and easy proofs are presented that a hyperbolic linear homeomorphism of a Banach space admits the shadowing.},
author = {Jerzy Ombach},
journal = {Annales Polonici Mathematici},
keywords = {hyperbolic; shadowing; pseudo-orbit; contraction; expansive; hyperbolic linear homeomorphism; Banach space; shadowing property},
language = {eng},
number = {3},
pages = {253-258},
title = {The simplest shadowing},
url = {http://eudml.org/doc/262250},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Jerzy Ombach
TI - The simplest shadowing
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 3
SP - 253
EP - 258
AB - Two different and easy proofs are presented that a hyperbolic linear homeomorphism of a Banach space admits the shadowing.
LA - eng
KW - hyperbolic; shadowing; pseudo-orbit; contraction; expansive; hyperbolic linear homeomorphism; Banach space; shadowing property
UR - http://eudml.org/doc/262250
ER -

References

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  1. [1] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math. 470, Springer, 1975. Zbl0308.28010
  2. [2] M. C. Irwin, Smooth Dynamical Systems, Academic Press, 1980. Zbl0465.58001
  3. [3] S. Kakubari, A note on a linear homeomorphism on ℝ n with the pseudo-orbit tracing property, Sci. Rep. Niigata Univ. Ser. A 23 (1987), 35-37. Zbl0666.54022
  4. [4] A. Katok, Local properties of hyperbolic sets (in Russian), appendix to the Russian edition of: Z. Nitecki, Differentiable Dynamics, Mir, Moscow, 1975. 
  5. [5] K. Meyer and G. Sell, An analytic proof of the Shadowing Lemma, Funkc. Ekvac. 30 (1987), 127-133. Zbl0643.58015
  6. [6] A. Morimoto, Some stabilities of group automorphisms, in: Manifolds and Lie Groups, Progr. Math. 14, Birkhäuser, 1981, 283-299. 
  7. [7] J. Ombach, The Shadowing Lemma in the linear case, Univ. Iagell. Acta Math., to appear. Zbl0831.58043
  8. [8] M. Shub, Global Stability of Dynamical Systems, Springer, 1987. 

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