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Prog. Theor. Phys. Vol. 101 No. 5 (1999) pp. 1181-1185

[ Full Text PDF : FREE ACCESS (91K) ]

Letters

Exponentially Small Oscillation of 2-Dimensional Stable and Unstable Manifolds in 4-Dimensional Symplectic Mappings

Yoshihiro Hirata,*) Kazuhiro Nozaki and Tetsuro Konishi

Department of Physics, Nagoya University, Nagoya 464-8602, Japan

(Received January 6, 1999)

Abstract:

The homoclinic bifurcation of 4-dimensional symplectic mappings is studied asymptotically. We construct 2-dimensional stable and unstable manifolds near sub-manifolds that experience exponentially small splitting, and successfully obtain exponentially small oscillating terms in these 2-dimensional manifolds.


URL : http://ptp.ipap.jp/link?PTP/101/1181/
DOI : 10.1143/PTP.101.1181


*)E-mail: yhirata@allegro.phys.nagoya-u.ac.jp

[ Full Text PDF : FREE ACCESS (91K) ] Citation:

References:

  1. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
  2. V. F. Lazutkin, I. G. Shachmannski and M. B. Tabanov, Physica 40D (1989), 235[Elsevier].
  3. V. G. Gelfreich, V. F. Lazutkin and N. V. Svanidze, Physica 71D (1994), 82[Elsevier].
  4. V. Hakim and K. Mallick, Nonlinearity 6 (1993), 57[CrossRef].
  5. A. Tovbis, M. Tsuchiya and C. Jaffé, preprint (1994).
  6. A. Tovbis, M. Tsuchiya and C. Jaffé, Chaos 8 (1998), 665.
  7. K. Nakamura and M. Hamada, J. of Phys. A29 (1996), 7315.
  8. V. G. Gelfreich and D. K. Sharomov, Phys. Lett. A197 (1995), 139.
  9. Y. Hirata and T. Konishi, http://xxx.lanl.gov/abs/chao-dyn/9802009.
  10. Y. Hirata, K. Nozaki and T. Konishi, in preparation.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 102 No. 3 (1999) pp. 701-706 :
    The Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings
    Yoshihiro Hirata, Kazuhiro Nozaki and Tetsuro Konishi
  2. Progress of Theoretical Physics Vol. 102 No. 5 (1999) pp. 937-946 :
    Dynamics near Resonance Junctions in Hamiltonian Systems
    Shin-itiro Goto and Kazuhiro Nozaki
  3. Progress of Theoretical Physics Vol. 107 No. 4 (2002) pp. 637-654 :
    Random Wandering around Homoclinic-Like Manifolds in a Symplectic Map Chain
    Shin-itiro Goto, Kazuhiro Nozaki and Hiroyasu Yamada
  4. Progress of Theoretical Physics Vol. 116 No. 4 (2006) pp. 631-668 :
    Reconnection of Unstable/Stable Manifolds of the Harper Map
    Shigeru Ajisaka and Shuichi Tasaki

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