Repeller structure in a hierarchical model. 1. Topological properties

Year: 1991

Authors: Livi R., Politi A., Ruffo S.

Autors Affiliation: Dipartimento di Fisica, Universitą di Firenze, 50125 Firenze, Italy;
Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy;
Dipartimento di Chimica, Universitą della Basilicata, Potenza, Italy;
Istituto Nazionale di Fisica Nucleare, Sez. di Firenze, Italy

Abstract: The repeller associated with the renormalization dynamics of the spectral problem of a hierarchical tight-binding Schrodinger 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 rate R 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 for R < 2. Finally, we show the existence of a pointlike component of the spectrum located at its upper extremum for R < 1 and we present the associated wavefunctions. Journal/Review: JOURNAL OF STATISTICAL PHYSICS

Volume: 65 (1-2)      Pages from: 53  to: 72

KeyWords: STRANGE REPELLERS; LOCALIZATION; SCHRODINGER OPERATOR; HIERARCHICAL STRUCTURES; RENORMALIZATION GROUP
DOI: 10.1007/BF01329850

Citations: 5
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