Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T00:36:29.154Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on the Ruelle operator and the invariant line fields problem: II

Published online by Cambridge University Press:  26 August 2005

PETER M. MAKIENKO
PETER M. MAKIENKO
Affiliation:
Instituto de Matematicas, Av. de Universidad s/N., Col. Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos, Mexico and Institute for Applied Mathematics, 9 Shevchenko str., Khabarovsk, Russia (e-mail: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Let R be a rational map. A critical point c is called summable if the series $\sum_i(1/(R^i)'(R(c)))$ is absolutely convergent. Under certain topological conditions on the postcritical set we prove that R cannot be structurally stable if it has a summable critical point $c \in J(R)$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 5 , October 2005 , pp. 1561 - 1581
Copyright
2005 Cambridge University Press

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.)