On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms View Full Text


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Article Info

DATE

1994-03

AUTHORS

Giancarlo Benettin, Antonio Giorgilli

ABSTRACT

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 orders to integrate a Hamiltonian systemK, 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 fromK, but turns out to be ε5 close to it. Special attention is devoted to numerical integration for scattering problems. More... »

PAGES

1117-1143

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02188219

DOI

http://dx.doi.org/10.1007/bf02188219

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1045098794


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