Lagrangian singularities of invariant tori of Hamiltonian systems with two degrees of freedom
type: Item
instance of: scholarly article
title: Lagrangian singularities of invariant tori of Hamiltonian systems with two degrees of freedom
zbMATH Open document ID: 0675.58016
DOI: 10.1007/BF01389043
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143703
review text: The following main statement is proved, besides another, for the 2-torus \(T^ 2={\mathbb{R}}^ 2/2\pi {\mathbb{Z}}^ 2\). Theorem. Let L be an incompressible torus of class \(C^ 3\) imbedded in the hypersurface \(M=\{x\in T^*X:\) \(H(x)=h\), H being the Hamiltonian function\(\}\) (i.e. a torus whose imbedding into M induces a monomorphism of the fundamental groups \(\pi_ 1(L)\) to \(\pi_ 1(M))\) which is a Lagrangian manifold of \(T^*T^ 2\). If L has no closed orbits of the Hamiltonian flow then a natural projection \(\theta\) : \(T^*T^ 2\to T^ 2\) restricted to L is a diffeomorphism.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 4105903
zbMATH Keywords: Lagrangian singularities
zbMATH Keywords: Lagrangian manifold
zbMATH Keywords: Hamiltonian flow
author: Misha Bialy
author: Leonid Polterovich
reviewed by: Jan Andres
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4105903