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.
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This research is supported by the National Natural Science Foundation of China
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Liu, PD. Stability of orbit spaces of endomorphisms. Manuscripta Math 93, 109–128 (1997). https://doi.org/10.1007/BF02677460
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DOI: https://doi.org/10.1007/BF02677460