On the construction of transformations of linear hamiltonian systems to real normal forms

Eric Butcher, S. C. Sinha

Research output: Contribution to journalArticle

Abstract

A technique for constructing the transformations to real Hamiltonian normal forms of linear Hamiltonian systems via permutation matrices is presented. In particular, a method is shown for obtaining the symplectomorphism between the symplectic basis of the real Jordan form to the standard symplectic basis in which the real Hamiltonian normal form resides. All possible degeneracies are accounted for since the algebraic and geometric multiplicities of nonsemisimple eigenvalues are not restricted, including the "difficult" cases of zero and imaginary eigenvalues. Since the normal forms are not unique, several possible arrangements of the suggested transformations are given which result in the various normal forms derived previously as well as in a few new ones for degenerate cases which have not appeared before.

Original languageEnglish (US)
Pages (from-to)2177-2191
Number of pages15
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume10
Issue number9
StatePublished - Sep 2000
Externally publishedYes

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Hamiltonians
Normal Form
Hamiltonian Systems
Linear Systems
Jordan Form
Eigenvalue
Permutation Matrix
Arrangement
Multiplicity
Zero

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

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