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Invariant normalization of non-autonomous Hamiltonian systems

✍ Scribed by V.F. Zhuravlev

Book ID
104142253
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
574 KB
Volume
66
Category
Article
ISSN
0021-8928

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✦ Synopsis

A new algorithm is proposed for reducing non-autonomous Hamiltonian systems to normal Birkhoff form. The criterion for the normal form is the condition that the vector fields of the perturbed and unperturbed parts of the system should commute. The invariant character of the criterion enables the system to be normalized in a unified way, without first simplifying the unperturbed part and without distinguishing between resonance and non-resonance, or autonomous and non-autonomous, cases. The whole algorithm reduces to a one-dimensional recurrence formula. The result is obtained by using the Campbell-Hausdorff formula for the ring of asymptotic forms, as well as the solution of a homological equation in the form of a quadrature. Three examples are considered to illustrate the various special features of the new algorithm. One of the examples is of interest for nuclear magnetic resonance theory.

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