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Full Description
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.
Contents
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.
