The Semi Classical Maupertuis-jacobi Correspondance for Quasi-periodic Hamiltonian Flows
نویسنده
چکیده
We extend to the semi-classical setting the Maupertuis-Jacobi correspondance for a pair of hamiltonians (H(x, hDx),H(x, hDx). If H(p, x) is completely integrable, or has merely has invariant diohantine torus Λ in energy surface E , then we can construct a family of quasi-modes for H(x, hDx) at the corresponding energy E. This applies in particular to the theory of water-waves in shallow water, and determines trapped modes by an island, from the knowledge of Liouville metrics.
منابع مشابه
Orthogonal Geodesic Chords, Brake Orbits and Homoclinic Orbits in Riemannian Manifolds
The study of solutions with fixed energy of certain classes of Lagrangian (or Hamiltonian) systems is reduced, via the classical Maupertuis–Jacobi variational principle, to the study of geodesics in Riemannian manifolds. We are interested in investigating the problem of existence of brake orbits and homoclinic orbits, in which case the Maupertuis– Jacobi principle produces a Riemannian manifold...
متن کاملWave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
The algebraic–geometric approach is extended to study evolution equations associated with the energy-dependent Schrödinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvarieties of Jacobi varieties. The general approach is demonstrated by using new parametrizations for constructing quasi-periodic solutions of the shallow-...
متن کاملThe separability and dynamical r-matrix for the constrained flows of Jaulent-Miodek hierarchy
We show here the separability of Hamilton-Jacobi equation for a hierarchy of integrable Hamiltonian systems obtained from the constrained flows of the Jaulent-Miodek hierarchy. The classical Poisson structure for these Hamiltonian systems is constructed. The associated r-matrices depend not only on the spectral parameters, but also on the dynamical variables and, for consistency, have to obey t...
متن کاملConvergence of a semi-discretization scheme for the Hamilton--Jacobi equation: a new approach with the adjoint method
We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergenc...
متن کاملThe Jacobi-Maupertuis Principle in Variational Integrators
In this paper, we develop a hybrid variational integrator based on the Jacobi-Maupertuis Principle of Least Action. The Jacobi-Maupertuis principle states that for a mechanical system with total energy E and potential energy V{q), the curve traced out by the system on a constant energy surface minimizes the action given by / y^2{E — V{q))ds where ds is the line element on the constant energy su...
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 2008