Please use this identifier to cite or link to this item:
https://hdl.handle.net/10216/99544
Author(s): | PINTO, AA RAND, DA |
Title: | CLASSIFYING C1+ STRUCTURES ON DYNAMICAL FRACTALS .1. THE MODULI SPACE OF SOLENOID FUNCTIONS FOR MARKOV MAPS ON TRAIN TRACKS |
Issue Date: | 1995 |
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. |
Subject: | Matemática Mathematics |
Scientific areas: | Ciências exactas e naturais::Matemática Natural sciences::Mathematics |
URI: | https://repositorio-aberto.up.pt/handle/10216/99544 |
Document Type: | Artigo em Revista Científica Internacional |
Rights: | restrictedAccess |
Appears in Collections: | FCUP - Artigo em Revista Científica Internacional |
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File | Description | Size | Format | |
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109064.pdf Restricted Access | 360.97 kB | Adobe PDF | Request a copy from the Author(s) |
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