Measures of Full Dimension on Self-Affine Graphs

  • Eric Olivier
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


For a compact subset of the 2-torus that is left invariant by an expanding diagonal endomorphism, the Hausdorff and the Minkowski dimensions may not coincide: this dimensional hiatus is possible whenever the x-axis and y-axis expansion rates differ. The variational principle for dimension ensures that the Hausdorff dimension of the invariant compact set is obtained as the Hausdorff dimension of invariant probability measures called the measures of full dimension: we shall investigate such measures on examples related to classical self-affine graphs.


Variational Principle Topological Entropy Invariant Probability Measure Ergodic Measure Adjacency Graph 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Université de ProvenceMarseille Cedex 03France

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