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Classifying C1+ structures on dynamical fractals: 2. Embedded trees

Published online by Cambridge University Press:  14 October 2010

A. A. Pinto  and
D. A. Rand
A. A. Pinto
Affiliation:
Faculdade de Ciencias, Universidade do Porto, 4000 Porto, Portugal
D. A. Rand
Affiliation:
Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
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Abstract

We classify the C1+α structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded geometry and with contact points. We used these results in an earlier paper to describe the moduli spaces of smooth conjugacy classes of expanding maps and Markov maps on train tracks. In later papers we will use those results to do the same for pseudo-Anosov diffeomorphisms of surfaces. These results are also used in the classification of renormalisation limits of C1+α diffeomorphisms of the circle.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 5 , October 1995 , pp. 969 - 992
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

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