Repeller structure in a hierarchical model. I. Topological properties View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1991-10

AUTHORS

R. Livi, A. Politi, S. Ruffo

ABSTRACT

The repeller associated with the renormalization dynamics of the spectral problem of a hierarchical tight-binding Schrödinger equation is studied. Analysis of escaping regions and of stable and unstable manifolds provide complementary descriptions of the recurrent set, whose structure undergoes relevant changes when the growth rateR of the potential barriers is modified. The minimal region containing the repeller is determined and the mechanism originating a Cantor set structure along the unstable manifold is revealed. The repeller is continuous along the stable manifold forR < 2. Finally, we show the existence of a pointlike component of the spectrum located at its upper extremum forR < 1 and we present the associated wavefunctions. More... »

PAGES

53-72

References to SciGraph publications

  • 1988-08. The spectrum of a one-dimensional hierarchical model in JOURNAL OF STATISTICAL PHYSICS
  • 1987-09. The spectrum of a quasiperiodic Schrödinger operator in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1987-12. Resistance and eigenstates in a tight-binding model with quasiperiodic potential in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1983-09. Strange objects in the complex plane in JOURNAL OF STATISTICAL PHYSICS
  • 1989-12. Cantor spectrum and singular continuity for a hierarchical Hamiltonian in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1991-10. Repeller structure in a hierarchical model. II. Metric properties in JOURNAL OF STATISTICAL PHYSICS
  • Journal

    TITLE

    Journal of Statistical Physics

    ISSUE

    1-2

    VOLUME

    65

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01329850

    DOI

    http://dx.doi.org/10.1007/bf01329850

    DIMENSIONS

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