There are No Structural Stable Axiom A 3-Diffeomorphisms with Dynamics "One-dimensional Surfaced Attractor-repeller"

被引:1
|
作者
Pochinka, O. [1 ]
机构
[1] HSE Univ, DSA Lab, Moscow, Russia
基金
俄罗斯科学基金会;
关键词
Structural stability; attractor; repeller; TOPOLOGICAL CLASSIFICATION; DIFFEOMORPHISMS;
D O I
10.1007/s00025-022-01824-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we study the structural stability of three-dimensional diffeomorphisms with source-sink dynamics. Here the role of source and sink is played by one-dimensional hyperbolic repeller and attractor. It is well known that in the case when the repeller and the attractor are solenoids (not embedded in the surface), the diffeomorphism is not structurally stable. The author proves that in the case when the attractor and the repeller are canonically embedded in a surface, the diffeomorphism is also not structurally stable.
引用
收藏
页数:21
相关论文
共 50 条
  • [31] A NEUTRON-SCATTERING STUDY OF SPIN DYNAMICS IN THE ONE-DIMENSIONAL PARAMAGNET CSMNBR3
    GAULIN, BD
    COLLINS, MF
    CANADIAN JOURNAL OF PHYSICS, 1984, 62 (11) : 1132 - 1138
  • [32] Spin dynamics in the one-dimensional S=1/2 Heisenberg antiferromagnet CuGeO3
    Zavidonov, AY
    Larionov, IA
    Itoh, M
    JOURNAL OF PHYSICS AND CHEMISTRY OF SOLIDS, 2001, 62 (1-2) : 357 - 360
  • [33] Spin dynamics in S=3/2 one-dimensional Heisenberg antiferromagnets CsVCl3 and CsVBr3
    Itoh, S
    Endoh, Y
    Kakurai, K
    Tanaka, H
    Bennington, SM
    Perring, TG
    Ohoyama, K
    Harris, MJ
    Nakajima, K
    Frost, CD
    PHYSICAL REVIEW B, 1999, 59 (22) : 14406 - 14416
  • [34] COMPUTER-SIMULATION OF THE MULTIPLE-QUANTUM DYNAMICS OF ONE-DIMENSIONAL, 2-DIMENSIONAL AND 3-DIMENSIONAL SPIN DISTRIBUTIONS
    SCRUGGS, BE
    GLEASON, KK
    CHEMICAL PHYSICS, 1992, 166 (03) : 367 - 378
  • [35] MAGNETO-STRUCTURAL CORRELATIONS IN THE QUASI ONE-DIMENSIONAL INDUCED MOMENT MAGNETS AFEX3
    VISSER, D
    HARRISON, A
    JOURNAL DE PHYSIQUE, 1988, 49 (C-8): : 1467 - 1468
  • [36] A feasible strategy for fabricating thermally stable CaSnO3:Eu3+ one-dimensional nanostructures with excellent luminescence
    Teng, Xue
    Li, Ning
    Liu, Xiaohan
    Shao, Hong
    Zhang, Xinran
    Li, Dan
    Yu, Wensheng
    Ma, Qianli
    Liu, Guixia
    Dong, Xiangting
    Dyes and Pigments, 2025, 239
  • [37] Classical properties in spin dynamics in the S=2 one-dimensional Heisenberg antiferromagnet, CsCrCl3
    Itoh, S
    Tanaka, H
    Bull, MJ
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2002, 71 (04) : 1148 - 1153
  • [38] ANALYTIC DYNAMICS OF THE ONE-DIMENSIONAL TIGHT-BINDING MODEL .3. NUMERICAL-STUDIES
    BRACKSTONE, MA
    LOVESEY, SW
    JOURNAL OF PHYSICS-CONDENSED MATTER, 1989, 1 (38) : 6793 - 6806
  • [39] E3TE3HAL, MIXED VALENCY TELLUROHALIDES OF GALLIUM AND INDIUM WITH ONE-DIMENSIONAL STRUCTURAL UNITS
    PAASHAUS, S
    KNIEP, R
    ANGEWANDTE CHEMIE-INTERNATIONAL EDITION IN ENGLISH, 1986, 25 (08): : 752 - 753
  • [40] SOLITON DYNAMICS IN THE ONE-DIMENSIONAL ANTI-FERROMAGNET TMMC [(CD3)4NMNCL3]
    BOUCHER, JP
    REGNAULT, LP
    ROSSATMIGNOD, J
    RENARD, JP
    BOUILLOT, J
    STIRLING, WG
    MEZEI, F
    PHYSICA B & C, 1983, 120 (1-3): : 241 - 249