The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2012-10, Vol.11 (2), p.231-275
Main Authors: Gouveia, Márcio Ricardo Alves, Colli, Eduardo
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
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Summary:Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-011-0058-5