On minimal decomposition of p-adic homographic dynamical systems

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成果类型：

期刊论文

作者：

Fan, Aihua;Fan, Shilei*;Liao, Lingmin;Wang, Yuefei

通讯作者：

Fan, Shilei

作者机构：

[Fan, Aihua; Fan, Shilei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.

[Fan, Aihua] Univ Picardie Jules Verne, CNRS, UMR 7352, LAMFA, F-80039 Amiens 1, France.

[Fan, Shilei] Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China.

[Liao, Lingmin] Univ Paris Est Creteil, CNRS, UMR 8050, LAMA, F-94010 Creteil, France.

[Wang, Yuefei] Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China.

通讯机构：

[Fan, Shilei] C

Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.

语种：

英文

关键词：

p-Adic dynamical system;Minimal component;Homographic map;Invariant measure

期刊：

Advances in Mathematics

ISSN：

0001-8708

年：

2014

卷：

257

页码：

92-135

DOI：

10.1016/j.aim.2014.02.007

基金类别：

The authors gratefully acknowledge the support of MCM, CAS, especially the support to the Program of Stochastics, Dimension and Dynamics. The CNRS program (PICS No. 5727 ) and NSF of China (Grant No. 10831008 and 11231009 ) are also acknowledged.

机构署名：

本校为第一且通讯机构

院系归属：

数学与统计学学院

摘要：

A homographic map in the field of p-adic numbers Q(p) is studied as a dynamical system on P-1(Q(p)), the projective line over Q(p). If such a system admits one or two fixed points in Q(p), then it is conjugate to an affine dynamics whose dynamical structure has been investigated by Fan and Fares. In this paper, we shall mainly solve the remaining case that the system admits no fixed point. We shall prove that this system can be decomposed into a finite number of minimal subsystems which are topologically conjugate to each other. All the minimal subsystems are exhibited and the unique invariant...

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On minimal decomposition of p-adic homographic dynamical systems

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