We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping ψε, analytic and ε-close to the identity, there exists an analytic autonomous Hamiltonian system, Hε such that its time-one mapping ΦHε differs from ψε by a quantity exponentially small in 1/ε. This result is applied, in particular, to the problem of numerical integration of Hamiltonian systems by symplectic algorithms; it turns out that, when using an analytic symplectic algorithm of order s to integrate a Hamiltonian system K, one actually follows "exactly," namely within the computer roundoff error, the trajectories of the interpolating Hamiltonian Hε, or equivalently of the rescaled Hamiltonian Kε=ε-1Hε, which differs from K, but turns out to be ε5 close to it. Special attention is devoted to numerical integration for scattering problems.
|Titolo:||On the Hamiltonian Interpolation of Near to the Identity Symplectic Mappings with Application to Symplectic Integration Algorithms|
GIORGILLI, ANTONIO (Ultimo)
|Data di pubblicazione:||mar-1994|
|Digital Object Identifier (DOI):||10.1007/BF02188219|
|Appare nelle tipologie:||01 - Articolo su periodico|