Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometr...Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.展开更多
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 li...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^g to Multiply form -∞ to ∞ M such that for any {y_i }_(i∈Z) ∈φ(M^g), y_(i+1) and f(y_i) 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 {x_i }_(i∈Z),there is a sequence of points {y_i }_(i∈Z) tracing it, in which y_(i+1) is obtained from f(y_i) by a motion along the center direction.展开更多
基金the National Natural Science Foundation of China (Grant No. 19731040)
文摘Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.
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^g to Multiply form -∞ to ∞ M such that for any {y_i }_(i∈Z) ∈φ(M^g), y_(i+1) and f(y_i) 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 {x_i }_(i∈Z),there is a sequence of points {y_i }_(i∈Z) tracing it, in which y_(i+1) is obtained from f(y_i) by a motion along the center direction.
