Fluctuation of ergodic sums over periodic orbits

CDSNS Colloquium
Thursday, January 17, 2019 - 10:00am
1 hour (actually 50 minutes)
Skiles 005
Penn State University
The fluctuations of ergodic sums by the means of global and local specifications on periodic points will be discussed. Results include a Lindeberg-type central limit theorems in both setups of specification. As an application, it is shown that averaging over randomly chosen periodic orbits converges to the integral with respect to the measure of maximal entropy as the period approaches infinity. The results also suggest to decompose the variances of ergodic sums according to global and local sources.