Stability of orbit spaces of endomorphisms
manuscripta mathematica(1997)
摘要
In this paper it is first proved that, for a hyperbolic set of a C 1 (non-invertible) endomorphism of a compact manifold, the dynamical structure of its orbit space (inverse limit space) is stable under C 1 -small perturbations and is semi-stable under C 0 -small perturbations. It is then proved that if an Axiom A endomorphism satisfies no-cycle condition then its orbit space is Θ-stable and R -stable under C 1 -small perturbations and is semi-Θ-stable and semi- R -stable under C 0 -small perturbations.
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关键词
58F10,58F15,58F11,Orbit space,hyperbolic set,Axiom A
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