Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T09:52:19.558Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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