Harper equation, the dissipative standard map and strange nonchaotic attractors: Relationship between an eigenvalue problem and iterated maps

Jukka A. Ketoja, Indubala I. Satija

Research output: Contribution to journalArticleScientificpeer-review

57 Citations (Scopus)

Abstract

The almost periodic eigenvalue problem described by the Harper equation is connected to other classes of quasiperiodic behavior; the dissipative dynamics on critical invariant tori and quasiperiodically driven maps. Firstly, the strong coupling limit of the supercritical Harper equation and the strong dissipation limit of the critical standard map play equivalent role in describing the universal characteristics of these systems. Secondly, a simple transformation is used to relate the Harper equation to a quasiperiodically forced one-dimensional map. In this case, the localized eigenstates of the supercritical Harper equation correspond to strange but nonchaotic attractors of the driven map. Furthermore, the existence of localization in the eigenvalue problem is associated with the appearance of homoclinic points in the corresponding map.

Original languageEnglish
Pages (from-to)70-80
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Volume109
Issue number1-2
DOIs
Publication statusPublished - 1 Jan 1997
MoE publication typeNot Eligible

Keywords

  • Harper equation
  • Quasiperiodicity
  • Renormalization localization
  • Standard map
  • Strange nonchaotic attractor

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