Orbital stability: Analysis meets geometry

Stephan De Bièvre, Francois Genoud, Simona Rota Nodari

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific

Abstract

We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and the corresponding momentum maps is proposed that allows us to highlight the interplay between (symplectic) geometry and (functional) analysis in the proofs of orbital stability of relative equilibria via the so-called energy-momentum method. The theory is illustrated with examples from finite dimensional systems, as well as from Hamiltonian PDE’s, such as solitons, standing and plane waves for the nonlinear Schrödinger equation, for the wave equation, and for the Manakov system.
Original languageEnglish
Title of host publicationNonlinear Optical and Atomic Systems
Subtitle of host publicationAt the Interface of Physics and Mathematics
EditorsC. Besse, J. Garreau
PublisherSpringer
Pages147-273
Number of pages127
ISBN (Electronic)978-3-319-19015-0
ISBN (Print)978-3-319-19014-3
DOIs
Publication statusPublished - 2015

Publication series

NameLecture Notes in Mathematics
PublisherSpringer International Publishing
Volume2146
ISSN (Electronic)0075-8434

Keywords

  • Mathematical Physics
  • Atomic, Molecular, Optical and Plasma Physics

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