THE DIMENSIONS OF SOME SELF-AFFINE LIMIT-SETS IN THE PLANE AND HYPERBOLIC SETS
UNSPECIFIED. (1994) THE DIMENSIONS OF SOME SELF-AFFINE LIMIT-SETS IN THE PLANE AND HYPERBOLIC SETS. JOURNAL OF STATISTICAL PHYSICS, 77 (3-4). pp. 841-866. ISSN 0022-4715Full text not available from this repository.
In this article we compute the Hausdorff dimension and box dimension (or capacity) of a dynamically constructed model similarity process in the plane with two distinct contraction coefficients. These examples are natural generalizations to the plane of the simple Markov map constructions for Canter sets on the line. Some related problems have been studied by different authors; however, those results are directed toward generic results in quite general situations. This paper concentrates on computing explicit formulas in as many specific cases as possible. The techniques of previous authors and ours are correspondingly very different. In our calculations, delicate number-theoretic properties of the contraction coefficients arise. Finally, we utilize the results for the model problem to compute the dimensions of some affine horseshoes in R(n), and we observe that the dimensions do not always coincide and their coincidence depends on delicate number-theoretic properties of the Lyapunov exponents.
|Item Type:||Journal Article|
|Subjects:||Q Science > QC Physics|
|Journal or Publication Title:||JOURNAL OF STATISTICAL PHYSICS|
|Publisher:||PLENUM PUBL CORP|
|Number of Pages:||26|
|Page Range:||pp. 841-866|
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