Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T10:33:00.216Z Has data issue: false hasContentIssue false
  • English
  • Français

ON INVARIANT LINE FIELDS

Published online by Cambridge University Press:  23 October 2000

ALBERT M. FISHER  and
MARIUSZ URBAŃSKI
ALBERT M. FISHER
Affiliation:
Department of Mathematics, IME-USP (Universidade de São Paulo), Caixa Postal 66281, CEP 05315-970, São Paulo, Brazil; e-mail: [email protected]
MARIUSZ URBAŃSKI
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5118, USA; e-mail: [email protected]
Get access

Abstract

It is shown that a rational function of degree [ges ] 2 admits an invariant line field with respect to some measure μ, which is an equilibrium state of a Hölder continuous potential whose topological pressure is greater than its supremum, only in very special cases when the Julia set is either a geometric circle or an interval, or totally disconnected and contained in a real-analytic curve.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 5 , September 2000 , pp. 555 - 570
Copyright
© The London Mathematical Society 2000

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.)