Open Conformal Systems and Perturbations of Transfer Operators

• Main Authors: Pollicott, Mark (Author), Urbański, Mariusz (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Lecture Notes in Mathematics, 2206
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Functional analysis.; Functions of complex variables.; Measure theory.; Operator theory.; Dynamical Systems and Ergodic Theory.; Functional Analysis.; Functions of a Complex Variable.; Operator Theory.; Measure and Integration.

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this...

Table of Contents:

• 1. Introduction
• 2. Singular Perturbations of Classical Original Perron–Frobenius Operators on Countable Alphabet Symbol Spaces
• 3. Symbol Escape Rates and the Survivor Set K(Un)
• 4. Escape Rates for Conformal GDMSs and IFSs
• 5. Applications: Escape Rates for Multimodal Maps and One-Dimensional Complex Dynamics.