Quantitative Poincaré recurrence in continued fraction dynamical system

DOI10.1007/S11425-011-4303-9zbMath1241.28007OpenAlexW2027463054MaRDI QIDQ424248

Bo Tan, Bao-Wei Wang, Li Peng

Publication date: 31 May 2012

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-011-4303-9

zbMATH Keywords

Hausdorff dimensionrecurrencecontinued fraction

Mathematics Subject Classification ID

Fractals (28A80) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (12)

Zero-one law of Hausdorff dimensions of the recurrent sets ⋮ Hausdorff dimensions of certain sets in terms of the Sylvester series ⋮ HAUSDORFF DIMENSIONS OF SOME EXCEPTIONAL SETS IN THE FIRST OSTROGRADSKY SERIES ⋮ ON THE LONGEST BLOCK FUNCTION IN CONTINUED FRACTIONS ⋮ The multifractal spectra of certain planar recurrence sets in the continued fraction dynamical system ⋮ Dimensions of recurrent sets in \(\beta\)-symbolic dynamics ⋮ Unnamed Item ⋮ The waiting spectra of the sets described by the quantitative waiting time indicators ⋮ On the intersections of localized Jarník sets and localized uniformly Jarník sets in continued fractions ⋮ On the recurrence rates of continued fractions ⋮ Best approximation of orbits in iterated function systems ⋮ The relative growth rate for partial quotients in continued fractions

Cites Work

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• A remark on the growth of the denominators of convergents
• Dimension of sets of sequences defined in terms of recurrence of their prefixes
• The Hausdorff dimension of recurrent sets in symbolic spaces
• Entropy and data compression schemes
• Conformal iterated function systems with applications to the geometry of continued fractions
• Recurrence spectrum in smooth dynamical systems
• Product structure of Poincaré recurrence

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