Stability of orbit spaces of endomorphisms
In this paper results concerning hyperbolic sets of diffeomorphisms are extended to \(C^1\) endomorphisms. Among other things it is proved that a hyperbolic set of a \(C^1\) endomorphism is weakly structurally stable and weakly topologically stable. Also some \(\Omega\) stability theorems are extended to endomorphisms satisfying some nondegeneracy conditions. In the theory put forward, the orbit space of the map considered plays an important role.
scientific article; zbMATH DE number 1038290
scientific article