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manuscripta mathematica

, Volume 93, Issue 1, pp 109–128 | Cite as

Stability of orbit spaces of endomorphisms

  • Pei-Dong Liu
Article

Abstract

In this paper it is first proved that, for a hyperbolic set of aC 1 (non-invertible) endomorphism of a compact manifold, the dynamical structure of its orbit space (inverse limit space) is stable underC 1-small perturbations and is semi-stable underC 0-small perturbations. It is then proved that if an Axiom A endomorphism satisfies no-cycle condition then its orbit space is Θ-stable andR-stable underC 1-small perturbations and is semi-Θ-stable and semi-R-stable underC 0-small perturbations.

1991 Mathematics Subject Classification

58F10 58F15 58F11 

Key words and phrases

Orbit space hyperbolic set Axiom A 

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Pei-Dong Liu
    • 1
  1. 1.Department of Mathematics and Institute of MathematicsPeking UniversityBeijingP. R. China

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