Hamiltonian and Lagrangian Flows on Center Manifolds

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.