Normal Modes in Symplectic Stratified Spaces
نویسنده
چکیده
We generalize theWeinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we significantly improve a result proved earlier jointly with Tokieda: we remove a strong technical hypothesis on the symmetry group.
منابع مشابه
The symplectic spaces that correspond to nonrational, nonsimple convex polytopes
We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold is a space locally modelled on R k modulo the action of a discrete, possibly infinite, group. The way strata are glued to each other also involves the actio...
متن کاملNonrational, Nonsimple Convex Polytopes in Symplectic Geometry
In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e., the strata are locally modeled by Rk modulo the action of a discrete, possibly infinite, group. Each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the or...
متن کاملConvex polytopes and quasilattices from the symplectic viewpoint
We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold is a space locally modelled on R k modulo the action of a discrete, possibly infinite, group. The way strata are glued to each other also involves the actio...
متن کاملThe Topological Structure of Contact and Symplectic Quotients
We show that if a Lie group acts properly on a co-oriented contact manifold preserving the contact structure then the contact quotient is topologically a stratified space (in the sense that a neighborhood of a point in the quotient is a product of a disk with a cone on a stratified space). As a corollary we obtain that symplectic quotients for proper Hamiltonian actions are topologically strati...
متن کاملLOCAL BASES WITH STRATIFIED STRUCTURE IN $I$-TOPOLOGICAL VECTOR SPACES
In this paper, the concept of {sl local base with stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999