# The simplest shadowing

Annales Polonici Mathematici (1993)

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

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topJerzy 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

top- [1] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math. 470, Springer, 1975. Zbl0308.28010
- [2] M. C. Irwin, Smooth Dynamical Systems, Academic Press, 1980. Zbl0465.58001
- [3] S. Kakubari, A note on a linear homeomorphism on ${\mathbb{R}}^{n}$ with the pseudo-orbit tracing property, Sci. Rep. Niigata Univ. Ser. A 23 (1987), 35-37. Zbl0666.54022
- [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. Zbl0643.58015
- [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. Zbl0831.58043
- [8] M. Shub, Global Stability of Dynamical Systems, Springer, 1987.

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