The Hausdorff dimension of the Smale-Williams solenoid with different contraction coefficients

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Abstract

In this paper we prove that the Hausdorff dimension of the Smale-Williams solenoid Ā with different contraction coefficients λ, μ is given by the formula dimH(Ā) = 1 + lig2/log(1/max(λ,μ)). Further, for λ,μ < 1/8 we prove that the Hausdorff dimension of each angular section is equal to lig2/log(1/max(λ,μ)).

Original languageEnglish
Pages (from-to)1221-1228
Number of pages8
JournalProceedings of the American Mathematical Society
Volume125
Issue number4
DOIs
Publication statusPublished - Jan 1 1997

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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