Open Conformal Systems and Perturbations of Transfer Operators

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Open Conformal Systems and Perturbations of Transfer Operators by Mark Pollicott, Mariusz Urbański, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mark Pollicott, Mariusz Urbański ISBN: 9783319721798
Publisher: Springer International Publishing Publication: February 5, 2018
Imprint: Springer Language: English
Author: Mark Pollicott, Mariusz Urbański
ISBN: 9783319721798
Publisher: Springer International Publishing
Publication: February 5, 2018
Imprint: Springer
Language: English

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 has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved.

The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, rational functions and meromorphic maps. 

Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved.

The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, rational functions and meromorphic maps. 

Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.

More books from Springer International Publishing

Cover of the book Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: Modelling and Benchmarking by Mark Pollicott, Mariusz Urbański
Cover of the book Relativistic Geodesy by Mark Pollicott, Mariusz Urbański
Cover of the book Creative Hubs in Question by Mark Pollicott, Mariusz Urbański
Cover of the book Group Sequential and Confirmatory Adaptive Designs in Clinical Trials by Mark Pollicott, Mariusz Urbański
Cover of the book Exploring the Mechanics of Chronic Inflation and Hyperinflation by Mark Pollicott, Mariusz Urbański
Cover of the book Taming the Wild Grape by Mark Pollicott, Mariusz Urbański
Cover of the book Homological Mirror Symmetry and Tropical Geometry by Mark Pollicott, Mariusz Urbański
Cover of the book Ad Hoc Networks by Mark Pollicott, Mariusz Urbański
Cover of the book Decision and Game Theory for Security by Mark Pollicott, Mariusz Urbański
Cover of the book Social Network Analysis - Community Detection and Evolution by Mark Pollicott, Mariusz Urbański
Cover of the book Mobile Networks for Biometric Data Analysis by Mark Pollicott, Mariusz Urbański
Cover of the book Path Coupling and Aggregate Path Coupling by Mark Pollicott, Mariusz Urbański
Cover of the book New Production Technologies in Aerospace Industry by Mark Pollicott, Mariusz Urbański
Cover of the book Current Challenges in Stability Issues for Numerical Differential Equations by Mark Pollicott, Mariusz Urbański
Cover of the book Animal Ethics in the Age of Humans by Mark Pollicott, Mariusz Urbański
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy