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

Dynamical cores of topological polynomials

Dynamical cores of topological polynomials

(p.27) Dynamical cores of topological polynomials
Frontiers in Complex Dynamics

Alexander Blokh

Lex Oversteegen

Ross Ptacek

Vladlen Timorin

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Princeton University Press

This chapter defines the (dynamical) core of a topological polynomial (and the associated lamination). This notion extends that of the core of a unimodal interval map. Two explicit descriptions of the core are given: one related to periodic objects and one related to critical objects. Topological polynomials are topological dynamical systems that generalize complex polynomials with locally connected Julia sets restricted to their Julia sets and considered up to topological conjugacy. This chapter aims to illustrate the analogy between the dynamics of topological polynomials on their cutpoints and cut-atoms and interval dynamics. For example, it is known that for interval maps, periodic points and critical points play a significant, if not decisive, role. This chapter thus attempts to establish similar facts for topological polynomials.

Keywords:   dynamical cores, topological polynomials, unimodal interval map, periodic objects, critical objects, interval dynamics

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.