连续双曲同构的稳定/不稳定整体性、周期点密度和反转性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-07-16 DOI:10.1088/1361-6544/ad6056

B Carvalho and E Rego

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引用次数: 0

摘要

我们讨论了 cw-双曲同构的稳定/不稳定全局性的不同规律性，并证明如果 cw-双曲同构具有连续的联合稳定/不稳定全局性，那么它的非漫游集中就有一组密集的周期点。为此，我们证明双曲 cw-metric（Artigue 等（2024 J. Differ. Equ.378 512-38）中引入）可以调整为自相似（如 Artigue（2018 Ergodic Theory Dyn. Syst.38 2422-46）），并且在这种情况下，连续联合稳定/不稳定全局是伪等距的。我们还证明了假设稳定/不稳定全等式的 cw-双曲同构的反转性。在环境空间是曲面的情况下，我们证明了当每个双渐近扇形都是正则时，cwF-双曲同构具有连续的联合稳定/不稳定全同性。

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Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms

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 Artigue et al (2024 J. Differ. Equ.378 512–38)) can be adapted to be self-similar (as in Artigue (2018 Ergodic Theory Dyn. Syst.38 2422–46)) 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 cwF-hyperbolic homeomorphism has continuous joint stable/unstable holonomies when every bi-asymptotic sector is regular.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.