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Analytic structure and integrability of dynamical systems
Author(s) -
Tabor Michael
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560220818
Subject(s) - integrable system , gravitational singularity , property (philosophy) , dynamical systems theory , extension (predicate logic) , analytic function , function (biology) , motion (physics) , dynamical system (definition) , mathematical analysis , mathematics , mathematical physics , classical mechanics , physics , statistical physics , pure mathematics , quantum mechanics , computer science , philosophy , epistemology , evolutionary biology , biology , programming language
The solutions to the equations of motion of certain dynamical systems are investigated as a function of complex time. The use of the “Painlevé property,” i.e., the property that the only movable singularities exhibited by the solution are poles, enables a prediction of system parameter values for which the system is integrable. The method is illustrated by a study of the Henon‐Heiles system. Extension of the analysis to movable branch points reveals at least one more integrable case. Further changes in analytic structure correlate with the onset of widespread chaos.