B. O. Stratmann M. Stadlbauer
A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory
Preprint series: Mathematica Gottingensis
MSC:
11J70 Continued fractions and generalizations, See also {11A55, 11K50}
11J83 Metric theory
Abstract: In this note we investigate radial limit sets of arbitrary regular
conformal interated function systems. We show that for each of
these
systems there exists a variety of finite hyperbolic subsystems
such that the spectrum made of the Hausdorff dimensions of the limit sets
of these subsystems is dense in the interval between $0$ and the
Hausdorff dimension of the given conformal iterated function system.
This result has interesting applications in conformal dynamics and
elementary fractal number theory.
Keywords: Conformal iterated function systems,Kleinian groups, Julia sets, fractal geometry F