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Prog. Theor. Phys. Vol. 63 No. 4 (1980) pp. 1190-1201

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Analytical Conditions for the Appearance of Homoclinic and Heteroclinic Points of a 2-dimensional Mapping

— The Case of the Hénon Mapping —

Hiroaki Daido

Department of Physics, Kyoto University, Kyoto 606

(Received November 21, 1979)

Abstract:

A method is proposed to obtain analytical conditions for the appearance of homoclinic and heteroclinic points of a class of 2-dimensional mappings with a small parameter. It consists of solving a functional equation, which is satisfied by invariant curves, perturbatively and combining the results with simple geometrical consideration. The mapping proposed by Hénon is treated here, for which it is also found that the appearance of heteroclinic points results in the disappearance of a strange attractor. The results are in good agreement with those of numerical simulations.


URL : http://ptp.ipap.jp/link?PTP/63/1190/
DOI : 10.1143/PTP.63.1190

[ Full Text PDF : FREE ACCESS (971K) ] Citation:

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References:

  1. R. M. May, Nature 261 (1976), 459[CrossRef].
  2. J. Guckenheimer, G. Oster and A. Ipaktchi, J. Math. Biol. 4 (1977), 101.
  3. K. Tomita and T. Kai, J. Stat. Phys. 21 (1979), 65.
  4. For example, D. R. J. Chillingworth, Differential Topology with a View to Applications (Pitman, London, 1977) and references cited therein.
  5. S. Smale, Bull. Am. Math. Soc. 73 (1967), 747.
  6. P. Holmes, preprint (1978) submitted to Proc. R. Soc.
  7. Y. Ueda, J. Stat. Phys. 20 (1979), 181[CrossRef].
  8. V. K. Mel'nikov, Trans. Moscow Math. Soc. 12 (1963), 1.
  9. M. Hénon, Commun. Math. Phys. 50 (1976), 69[CrossRef].
  10. R. Bridges and G. Rowlands, Phys. Lett. A 63 (1977), 189[CrossRef].
  11. S. D. Feit, Commun. Math. Phys. 61 (1978), 249[CrossRef].
  12. D. Ruelle and F. Takens, Commun. Math. Phys. 20 (1971), 167[CrossRef].
  13. J. H. Curry, preprint (1978), which appeared in revised form in, Commun. Math. Phys. 68 (1979), 129[CrossRef].
  14. D. Ruelle, in Proceedings of International Mathmatical Physics Conference, Rome, 1977, (to appear.)
  15. S. Grossmann and S. Thomae, Z. Naturforsch. a 32 (1977), 1353.
  16. K. Tomita and H. Daido, in preparation.
  17. D. S. Broomhead, Prog. Theor. Phys. 62 (1979), 1556[PTP].
  18. F. R. Marotto, Commun. Math. Phys. 68 (1979), 187[CrossRef].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 67 No. 6 (1982) pp. 1698-1723 :
    Period-Doubling Bifurcations and Associated Universal Properties Including Parameter Dependence
    Hiroaki Daido
  2. Progress of Theoretical Physics Vol. 71 No. 1 (1984) pp. 35-49 :
    Fractal Basin Structure
    Shinji Takesue and Kunihiko Kaneko
  3. Progress of Theoretical Physics Vol. 76 No. 4 (1986) pp. 752-767 :
    Characteristic Structures of Power Spectra in Periodic Chaos
    Takeshi Yoshida and Koji Tomita
  4. Progress of Theoretical Physics Vol. 77 No. 2 (1987) pp. 239-253 :
    Characteristic Structures of Power Spectra in Periodic Chaos. II
    Takeshi Yoshida and Koji Tomita

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