Beyond topological hyperbolicity: The L-shadowing property

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Artigue, Alfonso¹  Carvalho, Bernardo^2,3  Cordeiro, Welington⁴  Vieitez, Jose¹ 

[1] Univ Republ, Dept Matemat & Estadist Litoral, Gral Rivera 1350, Salto, Uruguay

[2] Univ Fed Minas Gerais, Dept Matemat, Av Antonio Carlos 6627,Campus Pampulha, Belo Horizonte, MG, Brazil

[3] Friedrich Schiller Univ Jena, Fak Math & Informat, Ernst Abbe Pl 2, D-07743 Jena, Germany

[4] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland

关键词: Topological;    Hyperbolicity;    L-shadowing;    Expansiveness;   

DOI  :  10.1016/j.jde.2019.09.052

来源: Elsevier

【 摘 要 】

In this paper we further explore the L-shadowing property defined in [20] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo-Anosov diffeomorphisms of the two-dimensional sphere satisfy this property. Homeomorphisms satisfying the L-shadowing property have a spectral decomposition where the basic sets are either expansive or contain arbitrarily small topological semi-horseshoes (periodic sets where the restriction is semiconjugate to a shift). To this end, we characterize the L-shadowing property using local stable and unstable sets and the classical shadowing property. We exhibit homeomorphisms with the L-shadowing property and arbitrarily small topological semi-horseshoes without periodic points. At the end, we show that positive finite-expansivity jointly with the shadowing property imply that the space is finite. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free