Jump to ContentJump to Main Navigation
Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
Users without a subscription are not able to see the full content.

Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 21 September 2021

Entropy for hyperbolic Riemann surface laminations I

Entropy for hyperbolic Riemann surface laminations I

Chapter:
(p.569) Entropy for hyperbolic Riemann surface laminations I
Source:
Frontiers in Complex Dynamics
Author(s):

Tien-Cuong Dinh

Viet-Anh Nguyen

Nessim Sibony

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0020

This chapter introduces a notion of entropy for possibly singular hyperbolic laminations by Riemann surfaces. It also studies the transverse regularity of the Poincaré metric and the finiteness of the entropy. The chapter first focuses on compact laminations, which are transversally smooth, before turning to the case of singular foliations, showing how the Poincaré metric on leaves is transversally Hölder continuous. In addition, the chapter considers the problem in the proof that the entropy is finite for singular foliations is quite delicate and requires a careful analysis of the dynamics around the singularities. Finally, the chapter discusses a notion of metric entropy for harmonic probability measures and gives some open questions.

Keywords:   entropy, Riemann surfaces, hyperbolic laminations, Poincaré metric, finiteness, compact laminations, singular foliations, metric entropy, harmonic probability measures

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.