Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T05:00:51.351Z Has data issue: false hasContentIssue false
  • English
  • Français

PARABOLIC RATIONAL MAPS

Published online by Cambridge University Press:  05 July 2001

NICOLAI HAYDN  and
STEFANO ISOLA
NICOLAI HAYDN
Affiliation:
Mathematics Department, University of Southern California, Los Angeles, CA 90089-1113, USA; [email protected]
STEFANO ISOLA
Affiliation:
Dipartimento di Matematica e Fisica, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy; [email protected]
Get access

Abstract

The paper studies the dynamics of rational maps with indifferent parabolic points by comparing their dynamical properties with those of their ‘jump transformation’ which is uniformly expanding on a non-compact set with infinite Markov partition. It establishes the spectral properties of a two-variables operator-valued function associated to the jump transformation and exploits their dynamical relevance to allow the analytic properties of the pressure, the escape rate from a neighbourhood of the Julia set and the asymptotic distribution of pre-images to be studied.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 673 - 689
Copyright
The London Mathematical Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)