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$J$-stability of expanding maps in non-Archimedean dynamics

Published online by Cambridge University Press:  20 June 2017

JUNGHUN LEE
JUNGHUN LEE*
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan email m12003v@math.nagoya-u.ac.jp
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Abstract

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The aim of this paper is to show $J$-stability of expanding rational maps over an algebraically closed, complete and non-Archimedean field of characteristic zero. More precisely, we will show that for any expanding rational map, there exists a neighborhood of it such that the dynamics on the Julia set of any rational map in the neighborhood is the same as the dynamics of the expanding rational map as a non-Archimedean analogue of a corollary of Mañé, Sad and Sullivan’s result [On the dynamics of rational maps. Ann. Sci. Éc. Norm. Supér. (4)16 (1983), 193–217] in complex dynamics.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 4 , April 2019 , pp. 1002 - 1019
Copyright
© Cambridge University Press, 2017 

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