When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points

作     者：JEZIERSKI Jerzy 

作者机构：Institute of Applications of Informatics and MathematicsWarsaw University of Life Sciences(SGGW)Warsaw 00-757Poland 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2017年第60卷第9期

页      面：1579-1590页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Science Center Poland(Grant No.UMO2014/15/B/ST1/01710) 

主　　题：periodic points Nielsen number fixed point index smooth maps Lie group 

摘      要：There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.