Lagrangian flows: The dynamics of globally minimizing orbits

被引：11

作者：

Mañé R. ^{[1
]}

机构：

[1] IMPA, 22460-320 Jardim Botânico, Estrada Dona Castorina

来源：

Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society | 1997年 / 28卷 / 2期

关键词：

Action Function; Special Solution; Forthcoming Paper; Closed Manifold; Simple Framework;

D O I：

10.1007/BF01233389

中图分类号：

学科分类号：

摘要：

The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications. We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma]. © 1997, Sociedade Brasileira de Matemática.

引用

页码：141 / 153

页数：12

共 7 条

[1]

Bangert V., Minimal Geodesics, Erg. Th. and Dyn. Sys., 10, pp. 263-287, (1990)

[2]

Carneiro M.J., On the Minimizing Measures of the Action of Autonomous Lagrangians, Nonlinearity, 8, 6, pp. 1077-1085, (1995)

[3]

Hedlund G.A., Geodesics on a two dimensional Riemannian manifold with periodic coefficients, Ann. of Math., 33, pp. 719-739, (1932)

[4]

Mane R., Generic Properties and Problems of Minimizing Measures, Nonlinearity, 9, 2, pp. 273-310, (1996)

[5]

Mather J., Action Minimizing Measures for Positive Lagrangian Systems, Math. Z., 207, pp. 169-207, (1993)

[6]

Mather J., Variational Construction of Connecting Orbits, Ann. Inst. Fourier, 43, pp. 1349-1386, (1993)

[7]

Morse M., A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc., 26, pp. 25-60, (1924)

← 1 →