Sub-harmonics for two-dimensional Hamiltonian systems
type: Item
instance of: scholarly article
title: Sub-harmonics for two-dimensional Hamiltonian systems
zbMATH Open document ID: 0942.37043
author: Alberto Abbondandolo
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2000-02-23T00:00:00Z
review text: The author proves the following result: Every asymptotically linear \(T\)-periodic Hamiltonian system in \(\mathbb{R}^2\) which has at least two periodic orbits must have infinitely many sub-harmonics, of course, in the presence of non-resonance conditions. The existence result is based on the Morse theory for the action developed by Conley and Zehnder. Note that the author's main result is strictly related to a recent result by Frank, proved by completely different methods.
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 37J50
zbMATH DE Number: 1406548
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: periodic orbits
zbMATH Keywords: sub-harmonics
zbMATH Keywords: Morse theory
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s000300050007
OpenAlex ID: W2013060332
DOI: 10.1007/S000300050007
description: scientific article; zbMATH DE number 1406548