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Differentiable structures of central Cantor sets

Published online by Cambridge University Press:  12 April 2001

RODRIGO BAMÓN ,
CARLOS G. MOREIRA ,
SERGIO PLAZA  and
JAIME VERA
RODRIGO BAMÓN
Affiliation:
Depto. de Matemática, Universidad de Chile, Casilla 653 Santiago, Chile (e-mail: rbamon@abello.dic.uchile.cl)
CARLOS G. MOREIRA
Affiliation:
IMPA, Estrada Dona Castorina 110, Jardim Botánico 22460-320, Rio de Janeiro, Brasil (e-mail: gugu@impa.br)
SERGIO PLAZA
Affiliation:
Depto. de Matemática, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile (e-mail: splaza@fermat.usach.cl)
JAIME VERA
Affiliation:
Depto. de Matemática, Facultad de Ciencias, Universidad Católica del Norte, Avda. Angamos 0610, Antofagasta, Chile (e-mail: jvera@socompa.cecun.ucn.cl)
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Abstract

Central Cantor sets form a class of symmetric Cantor sets of the real line. Here we give a complete characterization of the $C^{k + \alpha}$ regularity of these Cantor sets. We also give a classification of central Cantor sets up to global and local diffeomorphisms. Examples of central Cantor sets with special dynamical and measure-theoretical properties are also provided. Finally, we calculate the fractal dimensions of an arbitrary central Cantor set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 5 , October 1997 , pp. 1027 - 1042
Copyright
1997 Cambridge University Press

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