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

Published online by Cambridge University Press:  19 September 2008

Ya. B. Pesin
Ya. B. Pesin
Affiliation:
All-Union Extra-Mural Construction Engineering Institute, Sredne Kalitnikovskaja St., 30, Moscow, 109807, USSR
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 3 , September 1984 , pp. 405 - 420
Copyright
Copyright © Cambridge University Press 1984

References

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