A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory. (English) Zbl 1099.37043
Summary: We investigate radial limit sets of arbitrary regular conformal iterated 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.
MSC:
| 37F50 | Small divisors, rotation domains and linearization in holomorphic dynamics |
| 32H50 | Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables |
| 37F35 | Conformal densities and Hausdorff dimension for holomorphic dynamical systems |
| 28A78 | Hausdorff and packing measures |
| 37A45 | Relations of ergodic theory with number theory and harmonic analysis (MSC2010) |
| 11K55 | Metric theory of other algorithms and expansions; measure and Hausdorff dimension |
Keywords:
radial limit sets; conformal iterated function systems; finite hyperbolic subsystems; Hausdorff dimensionReferences:
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