WIAS Preprint No. 299, (1996)
Any set of irregular points has full Hausdorff dimension and full topological entropy
Authors
- Barreira, Luis
- Schmeling, Jörg
ORCID: 0000-0001-6956-9463
2010 Mathematics Subject Classification
- 58F15 58F11
Keywords
- Birkhoff averages, irregular points, local entropies, Lyapunov exponents, pointwise dimensions
DOI
Abstract
We prove, for subshifts of finite type, conformal repellers, and two-dimensional horseshoes, that the set of points where both the pointwise dimension, local entropy, Lyapunov exponents, and Birkhoff averages do not exist carries full topological entropy and full Hausdorff dimension. This follows from a much stronger statement formulated for a class of symbolic dynamical systems which includes subshifts with the specification property. Our proofs strongly rely on the multifractal analysis of dynamical systems and constitute the first mathematical application of this theory.
Appeared in
- Israel J. Math. 116 (2000), pp. 29--70.
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