Equivalence for lie transforms View Full Text


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Article Info

DATE

1974-12

AUTHORS

Jacques Henrard, Jacques Roels

ABSTRACT

The Lie transform method used in Perturbation Theory is based upon an intrinsic algorithm for transforming functions or vector fields by a transformation close to the identity. It can thus be viewed as a specialization of methods and results of differential geometry as is shown in the first part of this paper. In a second part we answer some of the questions left open in connection with the equivalence of the algorithms proposed by Hori and Deprit. From a formal point of view, the methods are shown to be equivalent for non-canonical as well as canonical transformations and a formula relating directly the two generating functions (or vector fields) is presented (formula (5.17)). On the other hand, the equivalence is shown to hold also in the ring ofp-differentiable functions. More... »

PAGES

497-512

References to SciGraph publications

  • 1969-03. Canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. Perturbation method in the theory of nonlinear oscillations in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1973. The Algorithm of the Inverse for Lie Transform in RECENT ADVANCES IN DYNAMICAL ASTRONOMY
  • 1970-03. On a perturbation theory using Lie transforms in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1971-09. Explicit recursive algorithms for the construction of equivalent canonical transformations in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. The equivalence of von Zeipel mappings and Lie transforms in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01229124

    DOI

    http://dx.doi.org/10.1007/bf01229124

    DIMENSIONS

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