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On the measurable dynamics of real rational functions
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Shen, Weixiao (2003) On the measurable dynamics of real rational functions. Ergodic Theory and Dynamical Systems, Vol.23 (No.3). pp. 957-983. doi:10.1017/S0143385702001311 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S0143385702001311
Abstract
Let f be a real rational function with all critical points on the extended real axis and of even order. Then:
(1) f carries no invariant line field on the Julia set unless it is doubly covered by an integral torus endomorphism (a Lattés example); and
(2) f|J(f) has only finitely many ergodic components.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Fluid dynamics, Teichmüller spaces, Julia sets, Geometry, Hyperbolic, Ergodic theory | ||||
Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0143-3857 | ||||
Official Date: | June 2003 | ||||
Dates: |
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Volume: | Vol.23 | ||||
Number: | No.3 | ||||
Page Range: | pp. 957-983 | ||||
DOI: | 10.1017/S0143385702001311 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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