Limiting Return Times Distribution for Invariant Measures

schedule le mardi 28 mai 2019 de 10h30 à 12h00

Organisé par : david Burguet et Pierre-Antoine Guiheneuf

Intervenant : Nicolai Haydn (.)
Lieu : salle 16.26.209

Sujet : Limiting Return Times Distribution for Invariant Measures

Résumé :

We consider a map acting on a space  that carries an invariant probability measure. For

a positive measure set the return time is by Kac's theorem on average the reciprocal of

the measure of the return set. We then take a nested sequence of positive measure sets

which contract to a zero measure set 􀀀 in the given space , and show that if the return

times distributions, when rescaled according to Kac's law, converge then the limit will

be a compound Poisson distribution. The simplest case is when the limiting set 􀀀 is a

single point in which case on obtains a regular Poisson distribution if the limiting point

is non-periodic and a Polya-Aeppli distribution if the limiting point is periodic. We then

apply this result to the synchronisation of coupled interval maps where the diagonal is

an invariant limiting set 􀀀. We given an expression for the coecients in the compound

Poisson distribution which in general is not Polya-Aeppli.

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