Linear stability of symplectic maps

Linear stability of symplectic maps

A general method is presented for analytically calculating linear stability limits for symplectic maps of arbitrary dimension in terms of the coefficients of the characteristic polynomial and the Krein signatures. Explicit results are given for dimensions 4, 6, and 8. The codimension and unfolding a...

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Veröffentlicht in:Journal of mathematical physics 1987-05, Vol.28 (5), p.1036-1051
Hauptverfasser: Howard, J. E., MacKay, R. S.
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Sprache:eng
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Exact sciences and technology
Geometry, differential geometry, and topology
Mathematical methods in physics
Physics
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container_title Journal of mathematical physics
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creator Howard, J. E.
MacKay, R. S.
description A general method is presented for analytically calculating linear stability limits for symplectic maps of arbitrary dimension in terms of the coefficients of the characteristic polynomial and the Krein signatures. Explicit results are given for dimensions 4, 6, and 8. The codimension and unfolding are calculated for all cases having a double eigenvalue on the unit circle. The results are applicable to many physical problems, including the restricted three‐body problem and orbital stability in particle accelerators.
doi_str_mv 10.1063/1.527544
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subjects Exact sciences and technology
Geometry, differential geometry, and topology
Mathematical methods in physics
Physics
title Linear stability of symplectic maps
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