$J$-stability of expanding maps in non-Archimedean dynamics. (20th June 2017)

• Record Type: Journal Article
• Authors: LEE, JUNGHUN
• Is Part Of: Ergodic theory and dynamical systems. Volume 39:Number 4(2019)
• Page Start: 1002
• Page End: 1019
• Publication Date: 2017-06-20
• Subjects: Ergodic theory -- Periodicals; Differentiable dynamical systems -- Periodicals; 515.42
• DOI: 10.1017/etds.2017.53
• Languages: English
• ISSNs: 0143-3857

Abstract

Abstract : 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.