rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Index Theory for Symplectic Paths with Applications
  name:
    name part: Long, Yiming.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: sz
    date issued: 2002
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xxiv, 380 pages)
  abstract: This book gives a systematic introduction to the index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems. Among the topics covered are the algebraic and topological properties of symplectic matrices and groups, the index theory for symplectic paths, relations with other Morse-type index theories, Bott-type iteration formulae, splitting numbers, precise index iteration formulae, various index iteration inequalities, and common index properties of finitely many symplectic paths. The applications of these concepts yield new approaches to some outstanding problems and important progress on their solutions. Particular attention is given to the minimal period solution problem of Hamiltonian systems, the existence of infinitely many periodic points of the Poincaré map of Lagrangian systems on tori, and the multiplicity and stability problems of closed characteristics on convex compact smooth hypersurfaces in 2n-dimensional euclidean vector space. Researchers, graduate and postgraduate students from a wide range of areas inside mathematics or physics will benefit from this monograph. Teachers of advanced courses in symplectic geometry or Hamiltonian systems will also find it an excellent textbook.
  note: by Yiming Long.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Global differential geometry
  subject:
    topic: Global differential geometry
  subject:
    topic: Mathematics
  classification: QA641-670
  classification: 516.36
  related item:
    title info:
      title: Progress in Mathematics ; ; 207
  identifier: 9783034881753 (electronic bk.)
  identifier: 3034881754 (electronic bk.)
  identifier: 9783034894661
  identifier: 303489466X
  identifier: 3034881754
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260422170448.2
    record identifier: in00003574971
    language of cataloging:
      language term: eng