On invariant line fields

Authors
Fisher, AM Urbanski, M
Citation
Am. Fisher et M. Urbanski, On invariant line fields, B LOND MATH, 32, 2000, pp. 555-570
Citations number
15
Categorie Soggetti
Mathematics
Journal title
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
ISSN journal
00246093 → ACNP
Volume
32
Year of publication
2000
Part
5
Pages
555 - 570
Database
ISI
SICI code
0024-6093(200009)32:<555:OILF>2.0.ZU;2-N
Abstract
It is shown that a rational function of degree greater than or equal to 2 a dmits an invariant line field with respect to some measure mu, which is an equilibrium state of a Holder continuous potential whose topological pressu re 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 an d contained in a real-analytic curve.