Il giorno 15 Novembre alle ore 14:00 in aula 3014 si terrà il seguente seminario:
Prof. Claudio Bonanno (Dip. Matematica, Univ. Pisa) “Extending the Birkhoff Ergodic Theorem to systems preserving an infinite measure”.
Abstract: It is known that many of the classical results on the statistical properties of a probability preserving transformation fail when the measure preserved by the system is infinite. This is for example the case of the Birkhoff Ergodic Theorem, whose statement becomes essentially vacuous in the infinite measure context. In addition, J. Aaronson proved that it’s impossible to recover a significant result for a general integrable observable. In this talk I will show recent results on the pointwise asymptotic behaviour of the Birkhoff sums both for integrable and non-integrable observables in the case of infinite measure preserving systems. The main tools are the mixing properties of the system and the method of trimmed sums. I will apply our results to the sums of the coefficients of some continued fraction algorithms. The talk is based on papers in collaboration with Tanja I. Schindler.
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