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Some Stabilities of Group Automorphisms

  • Akihiko Morimoto
Part of the Progress in Mathematics book series (PM, volume 14)

Abstract

Let φ:M→M be a homeomorphism of a metric space (M,d) with distance function d. A (double) sequence {xi}i∈M of points xi ∈ M is called a δ-pseudo-orbit of φ iff d(φ(xi),xi+1) ≤ δ for every i∈Z, where δ>0 is a constant (cf. [2]). Given ε>0, a δ-pseudo-orbit {xi} is called to be ε-traced by a point y∈M iff d(φi (y),xi)≤ε for every i≤Z. We shall call φ stochastically stable, iff for any ε>0 there exists δ>0 such that every δ-pseudo-orbit of φ can be ε-traced by some point y∈M.

Keywords

Riemannian Manifold Group Automorphism Stochastic Stability Linear Automorphism Jordan Canonical Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Akihiko Morimoto
    • 1
  1. 1.Nagoya UniversityChigusaku, Nagoya 464Japan

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