Weak convergence and averaging for ODE

被引：4

作者：

Evans, Lawrence C. ^{[1
]}

Zhang, Te ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 138卷

基金：

美国国家科学基金会;

关键词：

Weak convergence; Stabilization; Adiabatic invariance; GEOMETRY;

D O I：

10.1016/j.na.2015.10.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This mostly expository paper shows how weak convergence methods provide simple, elegant proofs of (i) the stabilization of an inverted pendulum under fast vertical oscillations, (ii) the existence of particle traps induced by rapidly varying electric fields and (iii) the adiabatic invariance of integral(Gamma) p dx for slowing varying planar Hamiltonian dynamics. Under an appropriate, but very restrictive, unique ergodicity assumption, the proof of (iii) extends also to many degrees of freedom. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：83 / 92

页数：10