A NONCONVENTIONAL STRONG LAW OF LARGE NUMBERS AND FRACTAL DIMENSIONS OF SOME MULTIPLE RECURRENCE SETS

DOI10.1142/S0219493711500237zbMath1255.60044arXiv1012.2799OpenAlexW2963409914MaRDI QIDQ2905266

Yuri Kifer

Publication date: 27 August 2012

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2799

zbMATH Keywords

strong law of large numbersdynamical systemsnonconventional ergodic averagesmixingales

Mathematics Subject Classification ID

Strong limit theorems (60F15) Generalizations of martingales (60G48) Ergodic theorems, spectral theory, Markov operators (37A30) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dimension theory of smooth dynamical systems (37C45)

Related Items (15)

Multifractal analysis of some multiple ergodic averages ⋮ Dimension spectrum for a nonconventional ergodic average ⋮ Nonconventional Poisson limit theorems ⋮ Nonconventional moderate deviations theorems and exponential concentration inequalities ⋮ A local limit theorem for a number of multiple recurrences generated by some mixing processes with applications to Young towers ⋮ Nonconventional limit theorems in averaging ⋮ Strong approximations for nonconventional sums and almost sure limit theorems ⋮ Nonconventional large deviations theorems ⋮ Poisson and compound Poisson approximations in conventional and nonconventional setups ⋮ Normal sequences with given limits of multiple ergodic averages ⋮ Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems ⋮ A nonconventional local limit theorem ⋮ Dimensions of some fractals defined via the semigroup generated by 2 and 3 ⋮ Dynamical systems under random perturbations with fast switching and slow diffusion: hyperbolic equilibria and stable limit cycles ⋮ A functional CLT for nonconventional polynomial arrays

Cites Work

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• On the frequency of partial quotients of regular continued fractions
• Hausdorff dimension of some continued-fraction sets
• Fractal Dimensions and Random Transformations
• Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C ² - Transformations
• Nonconventional limit theorems

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