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p-Adic Dynamics and Sullivan's No Wandering Domains Theorem

Published online by Cambridge University Press:  04 December 2007

Robert L. Benedetto
Robert L. Benedetto
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A. E-mail: benny@math.Rochester.edu
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Abstract

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In this paper we study dynamics on the Fatou set of a rational function φ ∈ $\overline {\Bbb{Q}}_p(z)$. Using a notion of ‘components’ of the Fatou set defined by Benedetto, we state and prove an analogue of Sullivan's No Wandering Domains Theorem for p-adic rational functions which have no wild recurrent Julia critical points.

Keywords

discrete dynamical systemp-adic fieldnon-Archimedean fieldwandering domain
Type
Research Article
Information
Compositio Mathematica , Volume 122 , Issue 3 , July 2000 , pp. 281 - 298
Copyright
© 2000 Kluwer Academic Publishers