Let f:X → X be a positively expansive map and let X be a compact connected metric space. Then f is topologically mixing and f has the pseudo-orbit-tracing property.
We study the space of positively expansive differentiable maps of a compact connected C ∞ Riemannian manifold without boundary. It is proved that （i） the C1-interior of the set of positively expansive differentiabl...We study the space of positively expansive differentiable maps of a compact connected C ∞ Riemannian manifold without boundary. It is proved that （i） the C1-interior of the set of positively expansive differentiable maps coincides with the set of expanding maps, and （ii） Cl-generically, a differentiable map is positively expansive if and only if it is expanding.展开更多
文摘Let f:X → X be a positively expansive map and let X be a compact connected metric space. Then f is topologically mixing and f has the pseudo-orbit-tracing property.
基金Supported by JSPD Gtant-in-Aid for Scientific Research (C)(Grant No.19540209)
文摘We study the space of positively expansive differentiable maps of a compact connected C ∞ Riemannian manifold without boundary. It is proved that （i） the C1-interior of the set of positively expansive differentiable maps coincides with the set of expanding maps, and （ii） Cl-generically, a differentiable map is positively expansive if and only if it is expanding.
