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Notations and basic facts on center manifolds
The linear theory
10 other sections not shown
action analytic applications assume axial variable canonical coordinates canonical coordinates q,p center manifold Mc center manifold reduction center manifold theory center space Chapter condition consider corresponding cross-section Darboux's theorem defined diffeomorphism differential equation dimensional eigenvalues elliptic problems elliptic variational problems Euler-Lagrange equations fiber derivative finite-dimensional G x g G-invariant given h(xi Hamiltonian system Hence imaginary axis implies invariant invertible Jordan chains Lagrangian flow Lagrangian problem Lagrangian system Legendre transform Lemma Lie bracket Lie group G linear operator locally regular manifold domain mapping Moreover natural reduction neighborhood nonlinear normal form Note obtain one-form Poisson bracket Poisson structure Proceedings projection method Proof reduced Hamiltonian system reduced Lagrangian reduced problem reduced symplectic structure reduced system reduction function relation restriction result satisfies Section spectral strong ellipticity submanifold subspace symmetry symplectic form symplectic manifold symplectic structure T°(G x Q tangent space two-form variational problem vector field