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A method of the dissipative Henon map renormalization

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Abstract

A mechanism for period doubling and transition to chaos for the dissipative Henon map is investigated. The renormalization group technique is used for that purpose. In the context of this technique, a special approach is developed that relates the renormalization procedure with the simpler problem of the renormalization of the conservative Henon map.

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References

  1. Strange Attractors, Ed. by Ya. G. Sinai and L. P. Shil’nikov (Mir, Moscow, 1981) [in Russian].

    Google Scholar 

  2. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: an Introduction (Editorial URSS, Moscow, 2001; Wiley, New York, 1989).

    Google Scholar 

  3. T. Y. Li and J. A. Yorke, “Period Three Implies Chaos,” Amer. Math. Monthly 82, 985 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  4. H. G. Schuster, Deterministic Chaos: An Introduction (VCH, Weinheim, Federal Republic of Germany, 1988; Mir, Moscow, 1988).

    Google Scholar 

  5. R. H. G. Hellemann, “Self-Generated Chaotic Behaviour in Nonlinear Mechanics,” in Fundamental Problems in Statistical Mechanics (North-Holland, Amsterdam, 1980), Vol. 5.

    Google Scholar 

  6. R. S. Mackay, Renormalization in Area-Preserving Maps: Ph. D. Thesis (Univ. Microfilms Inc., Ann Arbor, MI, Princeton, 1982.

    Google Scholar 

  7. V. Volterra Lecóns sur la theórie mathématique de la lutte pour la vie (Gauthier-Villars, Paris, 1931; Nauka, Moscow, 1976).

    Google Scholar 

  8. A. D. Bazykin, Nonlinear Dynamics of Interacting Populations (Inst. komp’yuternykh issledovanii, Izhevsk-Moscow, 2003) [in Russian].

    Google Scholar 

  9. V. V. Prasolov and Yu. P. Solov’ev, Elliptic Curves and Algebraic Equations (Faktorial, Moscow, 1997) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    Yu. V. Bibik & D. A. Sarancha

Authors
  1. Yu. V. Bibik
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  2. D. A. Sarancha
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Correspondence to Yu. V. Bibik.

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Original Russian Text © Yu.V. Bibik, D.A. Sarancha, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 11, pp. 1893–1908.

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Bibik, Y.V., Sarancha, D.A. A method of the dissipative Henon map renormalization. Comput. Math. and Math. Phys. 50, 1793–1807 (2010). https://doi.org/10.1134/S0965542510110035

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  • DOI: https://doi.org/10.1134/S0965542510110035

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