Jörg Schmeling

Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension

For subshifts of finite type, conformal repellers, and conformal horseshoes, we prove that the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages do not exist simultaneously, 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 a non-trivial mathematical application of this theory.

Symbolic dynamics for

More than 30 years ago Renyi [ 1 ] introduced the representations ofn real numbers with an arbitrary base

\beta

beta > 1

-shifts and self-normal numbers

as a generalization of then

Dimension and invertibility of hyperbolic endomorphisms with singularities

p

Entropy Preservation Under Markov Coding

-adic representations. One of the most studied problems in this field isn the link between expansions to base

Invariant sets with zero measure and full Hausdorff dimension

beta

Metric, Fractal Dimensional and Baire Results on the Distribution of Subsequences

and ergodic properties of then corresponding

Strongly mixing sequences of measure preserving transformations

beta

On the completeness of multifractal spectra

-shift. In this paper we will follow the bibliography of Blanchard [ 2 ] andn given an affirmative answer to a question on the size of the set of real numbersn