On the Persistence of Lower-Dimensional Tori in Reversible Systems with Hyperbolic-Type Degenerate Equilibrium Point Under Small Perturbations

被引：0
作者：
Xiaocai Wang
Xiaofei Cao
机构：
[1] Huaiyin Institute of Technology,Faculty of Mathematics and Physics
来源：
Acta Applicandae Mathematicae | 2021年 / 173卷
关键词：
Reversible systems; KAM iteration; Small perturbation; Degenerate lower dimensional tori; Topological degree theorem; 37J40; 34C27;
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摘要：
This paper focuses on the persistence of lower-dimensional tori in reversible systems with hyperbolic-type degenerate equilibrium point under small perturbations. Moreover, the dimension of degenerate variable is greater than or equal to 2. By KAM iteration and the Topological degree theorem, we prove that the invariant torus with given frequency persists under small perturbations.
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  • [1] Broer H.W.(1995)Unfoldings of quasi-periodic tori in reversible systems J. Dyn. Differ. Equ. 7 191-212
  • [2] Huitema G.B.(2007)Normal linear stability of quasi-periodic tori J. Differ. Equ. 232 355-418
  • [3] Broer H.W.(2009)Quasi-periodic stability of normally resonant tori Physica D 238 309-318
  • [4] Hoo J.(2016)Oscillatory motions for the restricted planar circular three body problem Invent. Math. 203 417-492
  • [5] Naudot V.(2018)Degenerate lower dimensional invariant tori in reversible systems Discrete Contin. Dyn. Syst. 38 3735-3763
  • [6] Broer H.W.(1998)Time-reversal symmetry in dynamical systems: a survey Physics D 112 1-39
  • [7] Ciocci M.C.(2001)On lower dimensional invariant tori in reversible systems J. Differ. Equ. 176 158-194
  • [8] Hanßmann H.(1967)Convergent series expansions for quasi-periodic motions Math. Ann. 169 136-176
  • [9] Vanderbauwhede A.(2014)Invariant manifolds at infinity of the RTBP and the boundaries of bounded motion Regul. Chaotic Dyn. 19 745-765
  • [10] Broer H.W.(1982)Conservation of quasiperiodic motions in reversible multifrequency systems Dokl. Akad. Nauk Ukr. SSR, Ser. A. 9 19-22
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