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Abstract: Let V be a 4-dimensional complex symplectic vector space. This paper classifies those connected linear algebraic subgroups of the symplectic group Sp(V ) that admit two independent rational invariants. As an application we show the non-integrability of a three degree of freedom Hamiltonian system. Key Words: Rational invariant, transcendence degree, linear algebraic group, symplectic group, monodromy group, galois group, Hamiltonian, non-integrability, fuchsian, linearized equations,... (Update)
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BibTeX entry: (Update)
R.C. Churchill, D.L. Rod, M.F. Singer, Group Theoretic Obstructions to Integrability, Ergod. Th. and Dynam. Sys 15(1995), 15-48. http://citeseer.ist.psu.edu/churchill95grouptheoretic.html More
@misc{ churchill95group,
author = "R. Churchill and D. Rod and M. Singer",
title = "Group Theoretic Obstructions to Integrability",
text = "R.C. Churchill, D.L. Rod, M.F. Singer, Group Theoretic Obstructions to
Integrability, Ergod. Th. and Dynam. Sys 15(1995), 15-48.",
year = "1995",
url = "citeseer.ist.psu.edu/churchill95grouptheoretic.html" }
Citations (may not include all citations):159 Foundations of Mechanics (context) - Abraham, Marsden - 1978
135 Introduction to Lie Algebras and Representation Theory (context) - Humphreys - 1980
122 Theory of Ordinary Differential Equations (context) - Coddington, Levinson - 1955
98 An Introduction to the Theory of Numbers (context) - Niven, Zuckerman et al. - 1991
69 Algebraic Topology: An Introduction (context) - Massey - 1989
62 Linear Algebraic Groups (context) - Humphreys - 1981
40 Linear Algebraic Groups (context) - Springer - 1981
34 An algorithm for solving second order linear homogeneous dif.. - Kovacic - 1986
33 An Introduction to Differential Algebra (context) - Kaplansky - 1976
31 Galois Groups of Second and Third Order Linear Differential .. - Singer, Ulmer - 1993
30 Liouvillian and Algebraic Solutions of Second and Third Orde.. - Singer, Ulmer - 1993
19 An outline of differential galois theory (context) - Singer - 1990
15 Linear Algebra (context) - Hoffman, Kunze - 1971
12 Lie Algebras and their Representations (context) - Varadarajan, Groups - 1990
11 Lectures on Riemann Surfaces (context) - Forster - 1981
[Article contains additional citations not shown here]
Documents on the same site (http://www4.ncsu.edu/eos/users/s/singer/www/ms_papers.html): More
Testing Reducibility of Linear Differential Operators: A Group.. - Singer (1995) (Correct)
On Ramis's solution of the local inverse problem of.. - Mitschi, Singer (1994) (Correct)
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