Although individual orbits of chaotic dynamical systems are by definition unpredictable, the
average behavior of typical trajectories can often be given a precise statistical description …

Stability of the spectrum for transfer operators Page 1 ANNALI DELLA SCUOLA NORMALE
SUPERIORE DI PISA Classe di Scienze GERHARD KELLER CARLANGELO LIVERANI …

The application of chaotic dynamics to signal processing tasks stems from the realization
that its complex behavior becomes tractable when observed from a statistical perspective …

arXiv:2211.14661v1 [math.PR] 26 Nov 2022 Page 1 Iterated Function Systems: A
Comprehensive Survey Ramen Ghosh ∗ Jakub Mareček † November 29, 2022 Abstract We …

Statistical properties of chaotic dynamical systems are difficult to estimate reliably. Using
long trajectories as data sets sometimes produces misleading results. It has been …

Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets
splitting for cocycles of non-invertible linear operators (such as transfer operators) over an …

Rigorous numerical investigation of the statistical properties of piecewise expanding maps{A
feasibility study Page 1 Rigorous numerical investigation of the statistical properties of …

We consider the approximation of absolutely continuous invariant measures (ACIMs) of
systems defined by random compositions of piecewise monotonic transformations …

We describe a framework in which it is possible to develop and implement algorithms for the
approximation of invariant measures of dynamical systems with a given bound on the error …

In this series of lectures I try to illustrate systematically what I call the “functional analytic
approach” to the study of the statistical properties of Dynamical Systems. The ideas are …