Quenched Linear Response: Random Hyperbolic Dynamics

Description

This lecture by the instructor covers the concept of quenched linear response for random hyperbolic dynamics. It discusses the main theorem, Anosov diffeomorphisms, random composition of maps, regularity assumptions, explicit examples, and abstract quenched statistical stability. The lecture also explores the definition of Gouëzel-Liverani spaces, properties of BP,9, annealed response, and the regularity of the variance in the Central Limit Theorem.

Official source

https://mediaspace.epfl.ch/media/0_6p5yfdp2

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Anosov diffeomorphism

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Symbolic dynamics

In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the shift operator. Formally, a Markov partition is used to provide a finite cover for the smooth system; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one covering set to another.

Nonlinear system

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