Asymptotic Expansions of Unstable and Stable Manifolds in Time-Discrete Systems.

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Author(s)

Abstract

By means of an updated renormalization method, we construct asymptotic expansions for unstable manifolds of hyperbolic fixed points in the double-well map and the dissipative Hénon map, both of which exhibit strong homoclinic chaos. In terms of the asymptotic expansion, a simple formulation is presented to give the first homoclinic point in the double-well map. Even a truncated expansion of the unstable manifold is shown to reproduce the well-known many-leaved (fractal) structure of the strange attractor in the Hénon map.

Journal

  • Progress of Theoretical Physics

    Progress of Theoretical Physics 105(1), 99-107, 2001

    THE PHYSICAL SOCIETY OF JAPAN

Codes

  • NII Article ID (NAID)
    130004540043
  • Text Lang
    ENG
  • ISSN
    0033-068X
  • Data Source
    J-STAGE 
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