94-124 Yakov Pesin, Howard Weiss

ON THE DIMENSION OF A GENERAL CLASS OF GEOMETRICALLY DEFINED DETERMINISTIC AND RANDOM CANTOR-LIKE SETS (131K, TeX) May 6, 94

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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.

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