The topological entropy for autonomous Lagrangian systems on compact manifolds whose fundamental groups have exponential growth

作     者：Fei Liu Fang Wang Weisheng Wu Fei Liu;Fang Wang;Weisheng Wu

作者机构：College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdao 266590China School of Mathematical SciencesCapital Normal UniversityBeijing 100048China Department of Applied MathematicsChina Agricultural UniversityBeijing 100083China 

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

年 卷 期：2020年第63卷第7期

页      面：1323-1338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 National Natural Science Foundation of China(Grant Nos.11301305 and 11571207) supported by the State Scholarship Fund from China Scholarship Council(CSC) supported by National Natural Science Foundation of China(Grant No.11701559) the Fundamental Research Funds for the Central Universities(Grant No.2018QC054) supported by National Natural Science Foundation of China(Grant No.11571387) 

主　　题：Euler-Lagrange flow positive topological entropy fundamental group exponential growth 

摘      要：In this article,we consider the topological entropy for autonomous positive definite Lagrangian systems on connected closed Riemannian manifolds whose fundamental groups have exponential *** prove that on each energy level E(x,v)=k with kc(L),where c(L)is Mane’s critical value,the EulerLagrange flow has positive topological *** extends the classical Dinaburg theorem from geodesic flows to general autonomous positive definite Lagrangian systems.