In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse ...In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse limit space） M^f of f is topologically quasi-stable under C^0-small perturbations in the following sense： For any covering endomorphism g C^0-close to f, there is a continuous map φ from M^9 to Π-∞^∞ M such that for any {yi}i∈z∈φ（M^9）, yi＋1 and f（yi） differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense： For any pseudo-orbit {xi}i∈z, there is a sequence of points {yi}i∈z tracing it, in which yi＋1 is obtained from f（yi） by a motion along the center direction.展开更多
基金supported by the National Natural Science Foundation of China(No.11371120)the High-level Personnel for Institutions of Higher Learning in Hebei Province(No.GCC2014052)the Natural Science Foundation of Hebei Province(No.A2013205148)
文摘In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse limit space） M^f of f is topologically quasi-stable under C^0-small perturbations in the following sense： For any covering endomorphism g C^0-close to f, there is a continuous map φ from M^9 to Π-∞^∞ M such that for any {yi}i∈z∈φ（M^9）, yi＋1 and f（yi） differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense： For any pseudo-orbit {xi}i∈z, there is a sequence of points {yi}i∈z tracing it, in which yi＋1 is obtained from f（yi） by a motion along the center direction.
