Statistics of close visits to the indifferent fixed point of an interval map

DOI10.1007/BF01048020zbMath1100.37502MaRDI QIDQ2499873

Pierre Collet, Antonio Galves

Publication date: 23 August 2006

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

Poisson processintermittencydecay of correlationsindifferent fixed pointmap of the entrance time

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Arcsine and Darling–Kac laws for piecewise linear random interval maps, Rare events for the Manneville-Pomeau map, Dispersing billiards with cusps: slow decay of correlations, Entry time statistics to different shrinking sets, Return- and hitting-time limits for rare events of null-recurrent Markov maps, Mixing limit theorems for ergodic transformations, Poisson approximation for the number of visits to balls in non-uniformly hyperbolic dynamical systems, ASYMPTOTICS FOR RETURN TIMES OF RANK-ONE SYSTEMS, Asymptotics for hitting times, Correlation decay and recurrence asymptotics for some robust nonuniformly hyperbolic maps, RECURRENCE TIME STATISTICS IN CHAOTIC DYNAMICS: MULTIPLE RECURRENCES IN INTERMITTENT CHAOS, POISSON PROCESSES FOR SUBSYSTEMS OF FINITE TYPE IN SYMBOLIC DYNAMICS, Hitting and return times in ergodic dynamical systems, Possible limit laws for entrance times of an ergodic aperiodic dynamical system., On rare and extreme events

Cites Work

• Some mathematical problems in the theory of quantum chaos
• Continuity of type-I intermittency from a measure-theoretical point of view
• Invariant measures for Markov maps of the interval
• Ergodic properties of invariant measures for piecewise monotonic transformations
• Probability approximations via the Poisson clumping heuristic
• Poisson limit law for Markov chains