Statistical properties of dynamics. Introduction to the functional analytic approach
arXiv:1510.02615
Abstract
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions will be addressed: *existence of a regular invariant measure; *Lasota Yorke inequalities and spectral gap; *decay of correlations and some limit theorem; *stability under perturbations of the system *linear response *random systems *hyperbolic systems. The point of view taken is to present the general construction and ideas needed to obtain these results in the simplest way. For this, some theorem is proved in a form which is weaker than usually known, but with an elementary and simple proof. These notes are intended for the Hokkaido-Pisa University summer course 2021.
I decided to make these lecture notes public because it will be cited in some research paper. I hope these will be useful for some reader. In this new version several new topics are added, with some original approach
References in corpus (2)
Cited by in corpus (7)
- Controlling the statistical properties of expanding maps
- Quadratic response of random and deterministic dynamical systems
- Self consistent transfer operators. Invariant measures, convergence to equilibrium, linear response and control of the statistical properties
- Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps
- Geometric properties of disintegration of measures
- Quantitative statistical stability for the equilibrium states of piecewise partially hyperbolic maps
- A spectral approach to quenched linear and higher-order response for partially hyperbolic dynamics