Connecting orbits near the adiabatic limit of Lagrangian systems with turning points
type: Item
instance of: scholarly article
title: Connecting orbits near the adiabatic limit of Lagrangian systems with turning points
zbMATH Open document ID: 1435.37089
DOI: 10.1134/S1560354717050021
author: A. V. Ivanov
published in: Regular and Chaotic Dynamics
publication date: 2018-02-06T00:00:00Z
review text: The author considers a natural Lagrangian system on a complete Riemannian manifold influenced by the action of a time-periodic force field with potential $U(q, t, e) = f(\varepsilon t) V(q)$ depending slowly on time. Under the condition that the factor $f(t)$ is periodic and vanishes at least at one point on the period, the author, in the adiabatic limit $\varepsilon\rightarrow0$, proves the existence of a set $\epsilon_h$ such that the system possesses a rich class of doubly asymptotic trajectories connecting points of $X_c$ for $\varepsilon \in \epsilon_h$, where $X_c$ denote a set of isolated critical points of $V(x)$ at which $V(x)$ distinguishes its maximum or minimum.
reviewed by: A. Benhassine
Mathematics Subject Classification ID: 37J46
Mathematics Subject Classification ID: 37J51
Mathematics Subject Classification ID: 37J39
Mathematics Subject Classification ID: 70K44
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 6835234
zbMATH Keywords: connecting orbits
zbMATH Keywords: homoclinic and heteroclinic orbits
zbMATH Keywords: nonautonomous Lagrangian system
zbMATH Keywords: singular perturbation
zbMATH Keywords: exponential dichotomy
MaRDI profile type: Publication
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full work available at URL: s1560354717050021
OpenAlex ID: W2759203213
description: scientific article; zbMATH DE number 6835234