Hamiltonian and Lagrangian Flows on Center Manifolds. With Applications to Elliptic Variational Problems.

Mielke, Alexander

ISBN 10: 354054710X / ISBN 13: 9783540547105

Editore: Berlin, Springer, 1991

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Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03174 354054710X Sprache: Englisch Gewicht in Gramm: 150.

Codice articolo 2489074

Dati bibliografici

• Titolo: Hamiltonian and Lagrangian Flows on Center Manifolds. With Applications to Elliptic Variational Problems.
• Editore: Berlin, Springer
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 354054710X
• ISBN 13: 9783540547105
• Rilegatura: Softcover
• Peso: 150 grammi
• Cataloghi dei venditori:
  • SA MATHEMATIK

Descrizione articolo

Riassunto

The theory of center manifold reduction is studied in thismonograph in the context of (infinite-dimensional) Hamil-tonian and Lagrangian systems. The aim is to establish a"natural reduction method" for Lagrangian systems to theircenter manifolds. Nonautonomous problems are considered aswell assystems invariant under the action of a Lie group (including the case of relative equilibria).The theory is applied to elliptic variational problemsoncylindrical domains. As a result, all bounded solutionsbifurcating from a trivial state can be described by areduced finite-dimensional variational problem of Lagrangiantype. This provides a rigorous justification of rod theoryfrom fully nonlinear three-dimensional elasticity.The book will be of interest to researchers working inclassical mechanics, dynamical systems, elliptic variationalproblems, and continuum mechanics. It begins with theelements of Hamiltonian theory and center manifold reductionin order to make the methods accessible to non-specialists,from graduate student level.

Contenuti

Notations and basic facts on center manifolds.- The linear theory.- Hamiltonian flows on center manifolds.- Hamiltonian systems with symmetries.- Lagrangian systems.- Nonautonomous systems.- Elliptic variational problems on cylindrical domains.- Capillarity surface waves.- Necking of strips.- Saint-Venant's problem.