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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rotation numbers for random dynamical systems on the circle


Authors: Weigu Li and Kening Lu
Journal: Trans. Amer. Math. Soc. 360 (2008), 5509-5528
MSC (2000): Primary 60H15; Secondary 34C35, 58F11, 58F15, 58F36
Published electronically: May 29, 2008
MathSciNet review: 2415083
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Abstract: In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on analytic conjugacy to a circle rotation.


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Additional Information

Weigu Li
Affiliation: School of Mathematics, Peking University, Beijing 100871, People’s Republic of China
Email: weigu@math.pku.edu.cn

Kening Lu
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: klu@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04619-9
PII: S 0002-9947(08)04619-9
Keywords: Rotation number, random maps of circle, random differential equations.
Received by editor(s): November 24, 2006
Published electronically: May 29, 2008
Additional Notes: This work was partially supported by NSF0200961, NSF0401708, and NSFC10371083 (second author) and NSFC10531010 and NNSF10525104 (first author).
Article copyright: © Copyright 2008 American Mathematical Society