Diffeomorphisms with infinitely many Smale horseshoes

被引：0
|
作者：
Zhang, Xu [1 ]
Chen, Guanrong [2 ]
机构：
[1] Shandong Univ, Dept Math, Weihai 264209, Shandong, Peoples R China
[2] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Peoples R China
来源：
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2024年 / 30卷 / 12期
关键词：
Smale horseshoe; hyperbolic invariant set; symbolic dynamical system; coexistence; REAL POLYNOMIAL DIFFEOMORPHISMS; MAXIMAL ENTROPY; HENON MAPS; HYPERBOLICITY; DYNAMICS; C-2;
D O I：
10.1080/10236198.2024.2368170
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A class of planar diffeomorphims is formulated, with infinitely many coexisting Smale horseshoes, where the Lebesgue measure of the parameters with such strange dynamics is infinite. On each horseshoe, there exists a uniformly hyperbolic invariant set, on which the map is topologically conjugate to the two-sided full-shift on two symbols. Moreover, the topological entropy is infinite in certain parameter regions.
引用
收藏
页码：1866 / 1884
页数：19
相关论文
共 50 条
  • [41] Global attractor and repeller of Morse-Smale diffeomorphisms
    Grines, V. Z.
    Zhuzhoma, E. V.
    Medvedev, V. S.
    Pochinka, O. V.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2010, 271 (01) : 103 - 124
  • [42] Classification of Smale diffeomorphisms of surfaces:: realisable geometric types
    Béguin, F
    ANNALES DE L INSTITUT FOURIER, 2002, 52 (04) : 1135 - +
  • [43] Morse-Smale Surfaced Diffeomorphisms with Orientable Heteroclinic
    A. Morozov
    O. Pochinka
    Journal of Dynamical and Control Systems, 2020, 26 : 629 - 639
  • [44] Smale Regular and Chaotic A-Homeomorphisms and A-Diffeomorphisms
    Medvedev, Vladislav S.
    Zhuzhoma, Evgeny V.
    REGULAR & CHAOTIC DYNAMICS, 2023, 28 (02): : 131 - 147
  • [45] On spectral decomposition of Smale-Vietoris axiom A diffeomorphisms
    Isaenkova, N.
    Zhuzhoma, E.
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2017, 32 (02): : 221 - 233
  • [46] Realization of Morse–Smale diffeomorphisms on 3-manifolds
    Ch. Bonatti
    V. Z. Grines
    O. V. Pochinka
    Proceedings of the Steklov Institute of Mathematics, 2017, 297 : 35 - 49
  • [47] On Smale diffeomorphisms close to pseudo-Anosov maps
    Lewowicz, Jorge
    Ures, Raul
    COMPUTATIONAL & APPLIED MATHEMATICS, 2001, 20 (1-2): : 187 - 194
  • [48] Global attractor and repeller of Morse-Smale diffeomorphisms
    V. Z. Grines
    E. V. Zhuzhoma
    V. S. Medvedev
    O. V. Pochinka
    Proceedings of the Steklov Institute of Mathematics, 2010, 271 : 103 - 124
  • [49] Morse-Smale Surfaced Diffeomorphisms with Orientable Heteroclinic
    Morozov, A.
    Pochinka, O.
    JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2020, 26 (04) : 629 - 639
  • [50] Morse-Smale diffeomorphisms with three fixed points
    E. V. Zhuzhoma
    V. S. Medvedev
    Mathematical Notes, 2012, 92 : 497 - 512
12345