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Computability of the packing measure of totally disconnected self-similar sets

Published online by Cambridge University Press:  06 February 2015

MARTA LLORENTE  and
MANUEL MORÁN
MARTA LLORENTE
Affiliation:
Dpt. Análisis Económico: Economía cuantitativa, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain email m.llorente@uam.es
MANUEL MORÁN
Affiliation:
Dpt. Análisis Económico I, Universidad Complutense de Madrid, Campus de Somosaguas, 28223 Madrid, Spain email mmoranca@ccee.ucm.es
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Abstract

We present an algorithm to compute the exact value of the packing measure of self-similar sets satisfying the so called Strong Separation Condition (SSC) and prove its convergence to the value of the packing measure. We also test the algorithm with examples that show both the accuracy of the algorithm for the most regular cases and the possibility of using the additional information provided by it to obtain formulas for the packing measure of certain self-similar sets. For example, we are able to obtain a formula for the packing measure of any Sierpinski gasket with contraction factor in the interval $(0,\frac{1}{3}]$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 5 , August 2016 , pp. 1534 - 1556
Copyright
© Cambridge University Press, 2015 

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