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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: afisher@ime.usp.br
MARIUSZ URBAŃSKI
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5118, USA; e-mail: urbanski@dynamics.math.unt.edu
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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

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