SEMINARIO DI SISTEMI DINAMICI

venerdì 16 gennaio 2009

ore 14.00

Scuola Normale Superiore

Pisa

(Conferenze - Centro De Giorgi)

Giulio Tiozzo

Harvard University, USA

Terrà  un seminario dal titolo:

“Spectral analysis of the Perron-Frobenius operator for

continued fractions”

Abstract

The -continued fraction transformations are a generalization of the lassical Gauss map generating continued fractions; the maps in this amily are piecewise expanding but in general non-Markov. Through a areful investigation of the spectral decomposition of the transfer perator one can prove ergodic-theoretical results such as a central imit theorem for BV observables. This implies, consistently with umerical data, that the distribution of Birkhoff sums for the metric ntropy is Gaussian. By extending such methods to perturbations of the original system, one can discuss the continuity in of the standard ariation of this Gaussian.

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