Paper Title:

Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems

Published on:

3 July 2023

Primary Category:

Dynamical Systems

Paper Authors:

Jason Atnip,

Gary Froyland,

Cecilia Gonzalez-Tokman,

Sandro Vaienti

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Develops quenched thermodynamic formalism for open random interval maps with holes

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Proves existence and uniqueness of random conformal and invariant measures

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Shows exponential decay of correlations for invariant measure

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Relates escape rate to difference in expected pressures

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Obtains Hausdorff dimension of survivor set from expected pressure

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Proves abstract perturbation formula for leading Lyapunov multipliers

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Applies perturbation theory to obtain quenched extreme value theory

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Proves quenched statistical limit theorems for equilibrium states

A more literal title describing the main contributions

The paper develops a framework for open random dynamical systems generated by interval maps with holes that terminate trajectories. Key results include proving existence and uniqueness of random conformal and invariant measures, exponential decay of correlations, relating the escape rate to pressures, and obtaining the Hausdorff dimension of the survivor set. The second part of the paper proves an abstract perturbation formula for leading Lyapunov multipliers of operator cocycles and applies it to obtain a quenched extreme value theory and statistical limit theorems.

Equilibrium states for discontinuous partially hyperbolic maps

Dynamics and applications of quasimorphisms

Limiting behavior of equilibrium states on countable Markov shifts

Brownian Motion on Harmonic Spaces

Disordered supersymmetric field theories with random couplings

Dynamically orthogonal approximation captures key dynamics in stochastic differential equations

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