Hamiltonian and Lagrangian flows on center manifolds
with applications to elliptic variational problems
by Alexander Mielke
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level.
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Subjects
Calculus of variations, Elliptic Differential equations, Hamiltonian systems, Lagrangian equations, Hamilton, système de, Calcul des variations, Flot hamiltonien, Variété centre, Problème variationnel elliptique, Flot lagrangien, Lagrange equations, Systèmes hamiltoniens, Elliptisches Variationsproblem, Zentrumsmannigfaltigkeit, Équations différentielles elliptiques, Hamiltonsches System, Lagrange, Équations de, Differential equations, elliptic, Mathematics, Global analysis (Mathematics), Analysis, Mathematical and Computational Physics Theoretical| Edition | Availability |
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Hamiltonian and Lagrangian flows on center manifolds: with applications to elliptic variational problems
1991, Springer-Verlag
in English
354054710X 9783540547105
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Includes bibliographical references (p. [133]-138) and index.
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