Multiplicity of characteristics with Lagrangian boundary values on symmetric star-shaped hypersurfaces
type: Item
instance of: scholarly article
title: Multiplicity of characteristics with Lagrangian boundary values on symmetric star-shaped hypersurfaces
zbMATH Open document ID: 1180.53079
author: Fei Guo
author: Chungen Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-04-29T00:00:00Z
review text: In the space \(\mathbb R^{2n}\) with the standard symplectic form, two Lagrangian subspaces are given together with a compact \(C^2\) hypersurface, which is star-shaped and symmetric with respect to the origin. It is proved that there is infinitely many Lagrangian orbits placed on the hypersurface, beginning on one Lagrangian subspace and ending on the other. This is a generalization of the result when two Lagrangian subspaces coincide, which is proved in \textit{F. Luo} and \textit{C. Liu} [Nonlinear Anal., Theory Methods Appl. 69, 1425--1436 (2008; Zbl 1153.37407)].
reviewed by: Milena Radnović
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 5549407
zbMATH Keywords: symmetric star-shaped hypersurfaces
zbMATH Keywords: Lagrangian orbits
zbMATH Keywords: \(\mathbb{Z}_2\)-index theory
zbMATH Keywords: Arnold's chord conjecture
zbMATH Keywords: multiplicity
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.11.061
OpenAlex ID: W1983384233
cites work: High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
cites work: Dual variational methods in critical point theory and applications
cites work: First steps in symplectic topology
cites work: Existence of multiple periodic orbits on star‐shaped hamiltonian surfaces
cites work: Lagrangian intersections, symplectic energy, and areas of holomorphic curves
cites work: The Lagrange intersections for \(({\mathbb{C}}P^ n,{\mathbb{R}}P^ n)\)
cites work: Q4692985
cites work: Cuplength estimates on lagrangian intersections
cites work: Morse theory for Lagrangian intersections
cites work: Q3641693
cites work: Multiplicity of Lagrangian orbits on symmetric star-shaped hypersurfaces
cites work: Lusternik-Schnirelman-theory for Lagrangian intersections
cites work: Cup-length estimate for Lagrangian intersections
cites work: Maslov-Type Index Theory For Symplectic Paths With Lagrangian Boundary Conditions
cites work: Multiple brake orbits in bounded convex symmetric domains
cites work: Q4409239
cites work: Holomorphic disks and the chord conjecture
cites work: Lagrangian intersection under Legendrian deformations
cites work: Q4850939
cites work: Q4714152
DOI: 10.1016/J.JMAA.2008.11.061
description: scientific article; zbMATH DE number 5549407