BLENDERS FOR A NON-NORMALLY HENON-LIKE FAMILY

被引：0
|
作者：
Kiriki, Shin [1 ]
Nakajima, Masaki [2 ]
机构：
[1] Kyoto Univ Educ, Dept Math, Fushimi Ku, Fukakusa Fujinomori 1, Kyoto 6128522, Japan
[2] Odessey Co Ltd, Chiyoda Ku, Tokyo 1006017, Japan
来源：
TAMKANG JOURNAL OF MATHEMATICS | 2010年 / 41卷 / 02期
关键词：
Robust transitive dynamics; heterodimensional cycles; Henon-like family; non-normal horseshoes; blender;
D O I：
10.5556/j.tkjm.41.2010.666
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A blender is an indispensable concept presented by Bonatti and Diaz [3] to study high-dimensional C-1-robust transitive dynamics around heterodimensional cycles. In this paper, we present a certain Henon-like family of real quadratic diffeomorphisms on R-3, which exhibits an phase transition from non-normal horseshoes to blenders. It can be observable from a rapidly jump of topological dimension for some projected stable segments in some characteristic region of R-3.
引用
收藏
页码：149 / 166
页数：18
相关论文
共 50 条
  • [1] Existence of blenders in a Henon-like family: geometric insights from invariant manifold computations
    Hittmeyer, Stefanie
    Krauskopf, Bernd
    Osinga, Hinke M.
    Shinohara, Katsutoshi
    NONLINEARITY, 2018, 31 (10) : R239 - R267
  • [2] Blenders in centre unstable Henon-like families: with an application to heterodimensional bifurcations
    Diaz, Lorenzo J.
    Kiriki, Shin
    Shinohara, Katsutoshi
    NONLINEARITY, 2014, 27 (03) : 353 - 378
  • [3] Boxing-in of a blender in a Henon-like family
    Hittmeyer, Stefanie
    Krauskopf, Bernd
    Osinga, Hinke M.
    Shinohara, Katsutoshi
    FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS, 2023, 9
  • [4] Merger of a Henon-like attractor with a Henon-like repeller in a model of vortex dynamics
    Kazakov, Alexey
    CHAOS, 2020, 30 (01)
  • [5] On a Homoclinic Origin of Henon-like Maps
    Gonchenko, S. V.
    Gonchenko, V. S.
    Shilnikov, L. P.
    REGULAR & CHAOTIC DYNAMICS, 2010, 15 (4-5): : 462 - 481
  • [6] ABUNDANCE OF NON-UNIFORMLY HYPERBOLIC HENON-LIKE ENDOMORPHISMS
    Berger, Pierre
    ASTERISQUE, 2019, (410) : 53 - 177
  • [7] The boundary of hyperbolicity for Henon-like families
    Cao, Yongluo
    Luzzatto, Stefano
    Rios, Isabel
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2008, 28 : 1049 - 1080
  • [8] Dynamics of deformed Henon-like map
    Gupta, Divya
    Chandramouli, V. V. M. S.
    CHAOS SOLITONS & FRACTALS, 2022, 155
  • [9] On the basin problem for Henon-like attractors
    Takahasi, Hiroki
    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2006, 46 (02): : 303 - 348
  • [10] Parameter exclusions in Henon-like systems
    Luzzatto, S
    Viana, M
    RUSSIAN MATHEMATICAL SURVEYS, 2003, 58 (06) : 1053 - 1092
12345