Possible limit laws for entrance times of an ergodic aperiodic dynamical system.

DOI10.1007/BF02784515zbMath1054.37001MaRDI QIDQ1860709

Yves Lacroix

Publication date: 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

return times

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items

Entry times distribution for mixing systems ⋮ The general asymptotic return-time process ⋮ The compound Poisson distribution and return times in dynamical systems ⋮ Entry times distribution for dynamical balls on metric spaces ⋮ Hitting times and periodicity in random dynamics ⋮ Universal behaviour of extreme value statistics for selected observables of dynamical systems ⋮ The optimal sink and the best source in a Markov chain ⋮ Poisson and compound Poisson approximations in conventional and nonconventional setups ⋮ The law of series ⋮ Statistics of Poincaré recurrences for maps with integrable and ergodic components ⋮ Entry and return times distribution ⋮ ASYMPTOTICS FOR RETURN TIMES OF RANK-ONE SYSTEMS ⋮ Asymptotics for hitting times ⋮ RETURN TIME STATISTICS OF INVARIANT MEASURES FOR INTERVAL MAPS WITH POSITIVE LYAPUNOV EXPONENT ⋮ Spontaneous clustering in theoretical and some empirical stationary processes ⋮ MATRIX TECHNIQUE REPRESENTATION FOR SECOND RETURN TIME ASYMPTOTICS ⋮ AN INTRODUCTION TO QUANTITATIVE POINCARÉ RECURRENCE IN DYNAMICAL SYSTEMS ⋮ A Poisson limit theorem for Gibbs–Markov maps ⋮ Hitting and return times in ergodic dynamical systems ⋮ Return-Time Statistics, Hitting-Time Statistics and Inducing ⋮ Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Central limit asymptotics for shifts of finite type
• Recurrence times and rates of mixing
• Statistics of return times: A general framework and new applications
• Statistics of close visits to the indifferent fixed point of an interval map
• Limit laws of entrance times for low-complexity Cantor minimal systems
• Toeplitz minimal flows which are not uniquely ergodic
• Poisson limit law for Markov chains
• Systems of finite rank
• Return time statistics via inducing
• Poisson law for Axiom A diffeomorphisms
• 0-1-sequences of Toeplitz type
• On the notion of recurrence in discrete stochastic processes
• Ergodic sets