Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 36, 2011, 21-45

A FAMILY OF SMOOTH CANTOR SETS

Ignacio Garcia

Universidad Nacional del Litoral, Departamento de Matemática (FIQ-UNL)
Instituto de Matemática Aplicada del Litoral (CONICET-UNL)
Santiago del Estero 2829, S3000AOM, Santa Fe, Argentina; nacholma 'at' gmail.com

Abstract. We show that the Cantor set C_p associated to the sequence {1/n^p}_n, p > 1, is a smooth attractor. Moreover, it is smoothly conjugate to the 2^-p-middle Cantor set. We also study the convolution of Hausdorff measures supported on these sets and the structure and size of the sumset C_p + C_q.

2000 Mathematics Subject Classification: Primary 28A80.

Key words: Dynamically defined Cantor sets, sums of Cantor sets, convolution of measures.

Reference to this article: I. Garcia: A family of smooth Cantor sets. Ann. Acad. Sci. Fenn. Math. 36 (2011), 21-45.

Full document as PDF file

doi:10.5186/aasfm.2011.3602

Copyright © 2011 by Academia Scientiarum Fennica