On the notion of the dimension with respect to a dynamical system

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Abstract

For the invariant sets of dynamical systems a new notion of dimension-the so-called dimension with respect to a dynamical system-is introduced. It has some common features with the general topological notion of the dimension, but it also reflects the dynamical properties of the system. In the one-dimensional case it coincides with the Hausdorff dimension. For multi-dimensional hyperbolic sets formulae for the calculation of our dimension are obtained. These results are generalizations of Manning's results obtained by him for the Hausdorff dimension in the two-dimensional case.

Original languageEnglish (US)
Pages (from-to)405-420
Number of pages16
JournalErgodic Theory and Dynamical Systems
Volume4
Issue number3
DOIs
StatePublished - Sep 1984

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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