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A more literal title describing the main contributions

Published on:

3 July 2023

Primary Category:

Dynamical Systems

Paper Authors:

Jason Atnip,

Gary Froyland,

Cecilia Gonzalez-Tokman,

Sandro Vaienti

Bullets

Key Details

Develops quenched thermodynamic formalism for open random interval maps with holes

Proves existence and uniqueness of random conformal and invariant measures

Shows exponential decay of correlations for invariant measure

Relates escape rate to difference in expected pressures

Obtains Hausdorff dimension of survivor set from expected pressure

Proves abstract perturbation formula for leading Lyapunov multipliers

Applies perturbation theory to obtain quenched extreme value theory

Proves quenched statistical limit theorems for equilibrium states

AI generated summary

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.

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