Limiting Entry and Return Times Distribution for Arbitrary Null Sets
| Autor: | Nicolai Haydn, Sandro Vaienti |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
010102 general mathematics
Diagonal Mathematical analysis Complex system Statistical and Nonlinear Physics Limiting Absolute continuity Poisson distribution 01 natural sciences symbols.namesake 0103 physical sciences symbols Cluster (physics) 010307 mathematical physics 0101 mathematics Special case Invariant (mathematics) Mathematical Physics Mathematics |
| Zdroj: | Communications in Mathematical Physics. 378:149-184 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-020-03795-0 |
| Popis: | We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the cluster sizes, where clusters consist of the portion of points that have finite return times in the limit where random return times go to infinity. In the special case of periodic points we recover the known Polya-Aeppli distribution which is associated with geometrically distributed cluster sizes. We apply this method to several examples the most important of which is synchronisation of coupled map lattices. For the invariant absolutely continuous measure we establish that the returns to the diagonal is compound Poisson distributed where the coefficients are given by certain integrals along the diagonal. |
| Databáze: | OpenAIRE |
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