Johannes Jaerisch

Induced topological pressure for countable state Markov shifts

We generalise Savchenkos definition of topological entropy for special flows over countable Markov shifts by considering the corresponding notion of topological pressure. For a large class of Holder continuous height functions not necessarily bounded away from zero, this pressure can be expressed by our new notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words, and we are able to set up a variational principle in this context. Investigating the dependence of induced pressure on the subset of words, we give interesting new results connecting the Gurevic and the classical pressure with exhaustion principles for a large class of Markov shifts. In this context we consider dynamical group extensions to demonstrate that our new approach provides a useful tool to characterise amenability of the underlying group structure.

REGULARITY OF MULTIFRACTAL SPECTRA OF CONFORMAL ITERATED FUNCTION SYSTEMS

We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is we determine to what extent the multifractal spectrum depends continuously on the cIFS and its thermodynamic potential. For this we introduce the no- tion of regular convergence for families of cIFS not necessarily sharing the same index set, which guarantees the convergence of the multifractal spectra on the interior of their domain. In particular, we obtain an Exhausting Principle for infinite cIFS allowing us to carry over results for finite to infinite systems, and in this way to establish a multifractal analysis without the usual regularity conditions. Finally, we discuss the connections to the λ-topology introduced by Roy and Urba´ nski.

Fractal models for normal subgroups of Schottky groups

For a normal subgroup

The arithmetic-geometric scaling spectrum for continued fractions

N

Recurrence and pressure for group extensions

of the free group

Group-extended Markov systems, amenability, and the Perron-Frobenius operator

\F_d

Pointwise Hölder exponents of the complex analogues of the Takagi function in random complex dynamics

with at least two generators we introduce the radial limit set

A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups

\Lr(N,\Phi)

Thermodynamic Formalism for Group-Extended Markov Systems with Applications to Fuchsian Groups

of

MULTIFRACTAL FORMALISM FOR EXPANDING RATIONAL SEMIGROUPS AND RANDOM COMPLEX DYNAMICAL SYSTEMS

N