Asymptotic Counting in Conformal Dynamical Systems
نویسندگان
چکیده
In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts finite type. We deal with two classes such systems: attracting and parabolic. The latter being treated means former. prove fairly complete asymptotic counting results for multipliers diameters associated preimages or periodic orbits ordered a natural geometric weighting. also corresponding Central Limit Theorems describing further features distribution their weights. These have direct applications to wide variety examples, including case Apollonian Circle Packings, Triangle, expanding parabolic rational functions, Farey maps, continued fractions, Mannenville-Pomeau Schottky groups, Fuchsian many more. This gives unified approach which both recovers known proves new results. Our is founded on spectral properties complexified Ruelle–Perron–Frobenius operators Tauberian theorems as used in classical problems prime number theory.
منابع مشابه
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2021
ISSN: ['1947-6221', '0065-9266']
DOI: https://doi.org/10.1090/memo/1327