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CLASSIFYING C1+ STRUCTURES ON DYNAMICAL FRACTALS .1. THE MODULI SPACE OF SOLENOID FUNCTIONS FOR MARKOV MAPS ON TRAIN TRACKS
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UNSPECIFIED (1995) CLASSIFYING C1+ STRUCTURES ON DYNAMICAL FRACTALS .1. THE MODULI SPACE OF SOLENOID FUNCTIONS FOR MARKOV MAPS ON TRAIN TRACKS. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 15 (Part 4). pp. 697-734. ISSN 0143-3857.
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Abstract
Sullivan's scaling function provides a complete description of the smooth conjugacy classes of cookie-cutters. However, for smooth conjugacy classes of Markov maps on a train track, such as expanding circle maps and train track mappings induced by pseudo-Anosov systems, the generalisation of the scaling function suffers from a deficiency. It is difficult to characterise the structure of the set of those scaling functions which correspond to smooth mappings. We introduce a new invariant for Markov maps called the solenoid function. We prove that for any prescribed topological structure, there is a one-to-one correspondence between smooth conjugacy classes of smooth Markov maps and pseudo-Holder solenoid functions. This gives a characterisation of the moduli space for smooth conjugacy classes of smooth Markov maps. For smooth expanding maps of the circle with degree d this moduli space is the space of Holder continuous functions on the space {O,..., d - 1}(N) satisfying the matching condition.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | ERGODIC THEORY AND DYNAMICAL SYSTEMS | ||||
Publisher: | CAMBRIDGE UNIV PRESS | ||||
ISSN: | 0143-3857 | ||||
Official Date: | August 1995 | ||||
Dates: |
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Volume: | 15 | ||||
Number: | Part 4 | ||||
Number of Pages: | 38 | ||||
Page Range: | pp. 697-734 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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