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.