The simplest shadowing

• Autorzy: Jerzy Ombach
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

hyperbolic; shadowing; pseudo-orbit; contraction; expansive

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 3
• Strony: 253-258

Daty

wydano

1993

otrzymano

1992-03-16

Twórcy

autor

Jerzy Ombach

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

Bibliografia

• [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 $ℝ^n$ 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.