Lie groups and dynamical systems - Summary

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Marc Roussel

Jun 1, 1992, 9:55:10 PM6/1/92
A little over a week ago, I asked the readers of this group for
pointers to applications of Lie groups to dynamical systems. I would
first like to apologize for taking so long to post a summary; I have
received many useful responses and have been derelict in my duty to
share what I have learned.
I owe a debt of gratitude to the following individuals who have
provided the information on which this posting is based:

jb...@BOURBAKI.MIT.EDU (Hans Crauel)
David Drysdale <> (Dave Elliott) (Henning Fernau) (William H. Jefferys) (B. Moghaddam)
Miriam Nadel <>

In return for your indulgence on my tardiness, I will attempt to
organize this summary in a way that would make library searches
relatively easy. That unfortunately means that I will have to divorce
the names of my benefactors from the actual information provided. I
hope that I can be forgiven for this small transgression too.
Some of the responses I received were quite detailed. If anyone
finds a particular interest in a specific item in the following list,
I will gladly pass along the relevant parts of the original letters.

Marc R. Roussel

KEYWORDS: Lie groups, differential equations
AUTHOR: Peter J. Olver
TITLE: Applications of Lie Groups to Differential Equations
DETAILS: Springer-Verlag (GTM series 107) 1986

KEYWORDS: Lie groups, differential equations, bifurcation theory, singularities
AUTHORS: Golubitsky and Schaeffer (vol. 1);
Golubitsky, Stewart and Schaeffer (vol. 2)
TITLE: Singularities & Groups in bifurcation theory (3 vols.)
DETAILS: Springer-Verlag (AMS series 51) 1985 (vol. 1);
Springer-Verlag (AMS series 69) 1988 (vol. 2);
vol. 3 may not yet be in print.

KEYWORDS: Lie groups, differential equations, bifurcation theory
AUTHOR: Sattinger
TITLE: Group Theoretic methods in bifurcation theory
DETAILS: Springer-Verlag (LNM series 762) 1979

KEYWORDS: Lie groups, Lie algebras, differential equations, physics,
mechanics, geometry
AUTHORS: Sattinger and Weaver
TITLE: Lie Groups and Algebras with Applications to Physics,
Geometry and Mechanics'
DETAILS: Springer-Verlag (AMS series 61)

KEYWORDS: Lie groups, physics
AUTHORS: Robert Hermann
TITLE: Lie Groups for Physicists

KEYWORDS: Lie groups, mechanics
AUTHORS: Abraham and Marsden
TITLE: Foundations of Mechanics

KEYWORDS: Lie groups, Lie derivatives, celestial mechanics, perturbation theory
AUTHOR: Andre Deprit

KEYWORDS: Lie groups, mechanics, Hamiltonian systems
AUTHORS: Guillemin and Sternberg
TITLE: Symplectic Techniques in Physics

KEYWORDS: Lie groups, Lie algebras, Schrodinger's equation
AUTHOR: van der Waerden

KEYWORDS: Lie groups, chemical reaction dynamics, control, lasers
AUTHORS: Rabitz and Beumee

KEYWORDS: Lie groups, control theory
AUTHORS: Colonius and Kliemann

KEYWORDS: Lie algebras, control theory
AUTHOR: Jeff Kantor

KEYWORDS: Lie algebras, automatic control theory
AUTHORS: Roger Brockett, Hector Sussmann, Vel Jurdjevic, Henry Hermes
and David Elliott

KEYWORDS: Lie groups, control theory, H-infinity control

KEYWORDS: Lie groups, fractals
AUTHOR: A. Goetz
TITLE: Bemerkungen {\"u}ber Hausdorffsche Masse und
Hausdorffsche Dimensionen in Lieschen Gruppen
JOURNAL: Colloquium Mathematicum, v. 5, pp. 55-65, 1958.

KEYWORDS: Lie groups, multiplicative ergodic theorem
AUTHORS: Furstenberg, Guivarc'h, Goldsheild and Margulis

KEYWORDS: Lie transformation groups, visual processing, perception
AUTHOR: D.D. Hoffman
TITLE: An Informal Historical Description of the "LTG/NP"
JOURNAL: Cahiers de Psychologie, vol 20, pp.139-150, 1977.

KEYWORDS: Lie transformation groups, vision, perception
AUTHOR: P.C. Dodwell
TITLE: The Lie Transformation Group Model of Visual Perception
JOURNAL: Perception & Psychophysics, vol. 34, no. 1, pp. 1-16, 1988.

KEYWORDS: Lie transformation groups, Lie differentiation, vision,
AUTHOR: T. Papathomas and B. Julesz
TITLE: Lie Differential Operators in Animal and Machine Vision
DETAILS: Proc. of the Conference "From Pixels To Features", Bonas, France, 1988.

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