Yakov Pesin, Howard Weiss
ON THE DIMENSION OF A GENERAL CLASS OF GEOMETRICALLY DEFINED
DETERMINISTIC AND RANDOM CANTOR-LIKE SETS
(131K, TeX)
ABSTRACT. In this paper we unify and extend many of the known results
on the dimensions of deterministic and random Cantor-like sets in
$\BbbR^n$ using their symbolic representation. We also construct
several new examples of such constructions that illustrate some new
phenomena. These sets are defined by geometric constructions with
arbitrary placement of subsets. We consider Markov constructions,
general symbolic constructions, nonstationary constructions, random
constructions (determined by a very general distribution), and
combinations of the above. One application to dynamical systems
is a counterexample to the $C^0$ version of the Ruelle-Eckmann
conjecture.