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Invariant Lagrange Submanifolds of Dissipative Systems

Summary: Invariant Lagrange Submanifolds of
Dissipative Systems
A. Agrachev
We study smooth solutions of modified Hamilton­Jacobi equations
dq , q) + u(q) = 0, q M, on a compact manifold M.
Let M be a compact Riemannian manifold of class Ck
, k 2, with
the Riemannian structure (, ) I-1
q , , , TqM, q M, where
Iq : T
q M TqM is a self-adjoint linear map such that the quadratic form
z z, Iqz , z T
q M, is positive definite.
Let V Ck
(M) and be a closed differential 1-form on M of class Ck
such that = 0, where is the covariant derivative of . We consider
the Hamiltonian function H Ck


Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)


Collections: Engineering; Mathematics