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

• 作者: Fang Wang Fei Liu Weisheng Wu
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（7）
• 页码范围: 1323-1338
• 页数: 16页
• 语种: 英文

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 growth.We prove that on each energy level E(x,v) =k with k ≥ c(L),where c(L) is Ma(n)é's critical value,the Euler-Lagrange flow has positive topological entropy.This extends the classical Dinaburg theorem from geodesic flows to general autonomous positive definite Lagrangian systems.