APPLICATIONS OF A RELATIVE VARIATIONAL PRINCIPLE TO DIMENSIONS OF NONCONFORMAL EXPANDING MAPS-Reference-Cited by-同舟云学术

APPLICATIONS OF A RELATIVE VARIATIONAL PRINCIPLE TO DIMENSIONS OF NONCONFORMAL EXPANDING MAPS

Published:2011-11-21 Issue:04 Volume:11 Page:643-679
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

YAYAMA YUKI¹

Affiliation:

1. Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120 Piso 7 Santiago, Chile

Abstract

Zhao and Cao (2008) showed the relative variational principle for subadditive potentials in random dynamical systems. Applying their result, we find the Hausdorff dimension of an n (≥3)-dimensional general Sierpiński carpet which has an irreducible sofic shift in symbolic representation and study an invariant ergodic measure of full Hausdorff dimension. These generalize the results of Kenyon and Peres (1996) on the Hausdorff dimension of an n-dimensional general Sierpiński carpet represented by a full shift.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493711003486

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