Title: Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms Show Chinese title

Title: 连续统双曲同胚的稳定/不稳定遍历、周期点密度和传递性

Abstract: We discuss different regularities on stable/unstable holonomies of cw-hyperbolic homeomorphisms and prove that if a cw-hyperbolic homeomorphism has continuous joint stable/unstable holonomies, then it has a dense set of periodic points in its non-wandering set. For that, we prove that the hyperbolic cw-metric (introduced in [9]) can be adapted to be self-similar (as in [6]) and, in this case, continuous joint stable/unstable holonomies are pseudo-isometric. We also prove transitivity of cw-hyperbolic homeomorphisms assuming that the stable/unstable holonomies are isometric. In the case the ambient space is a surface, we prove that a cw$_F$-hyperbolic homeomorphism has continuous joint stable/unstable holonomies when every bi-asymptotic sector is regular. Show Chinese abstract

Abstract: 我们讨论了cw-双曲同胚的稳定/不稳定流形的不同正则性，并证明如果一个cw-双曲同胚具有连续的联合稳定/不稳定流形，则它在非游荡集中有稠密的周期点。 为此，我们证明了超双曲cw度量（在[9]中引入）可以被调整为自相似（如[6]），在这种情况下，连续的联合稳定/不稳定流形是伪等距的。 我们还证明了当稳定/不稳定流形是等距的时候，cw-双曲同胚具有传递性。 在环境空间是曲面的情况下，我们证明了当每个双向渐近扇区都是正则的时候，一个cw$_F$-双曲同胚具有连续的联合稳定/不稳定流形。