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Summing up the Dynamics of Quadratic Hamiltonian Systems With a Center

Published online by Cambridge University Press:  20 November 2018

Janos Pal  and
Dana Schlomiuk
Janos Pal
Affiliation:
Département de mathématiques et de statistique and Centre de recherches mathématiques, Université de Montréal, C.P. 6128, succ., Centre-ville, Montréal, Québec, H3C 3J7
Dana Schlomiuk
Affiliation:
Département de mathématiques et de statistique and Centre de recherches mathématiques, Université de Montréal, C.P. 6128, succ., Centre-ville, Montréal, Québec, H3C 3J7
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Abstract

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In this work we study the global geometry of planar quadratic Hamiltonian systems with a center and we sum up the dynamics of these systems in geometrical terms. For this we use the algebro-geometric concept of multiplicity of intersection Ip(P,Q) of two complex projective curves P(x, y, z) = 0, Q(x,y,z) = 0 at a point p of the plane. This is a convenient concept when studying polynomial systems and it could be applied for the analysis of other classes of nonlinear systems.

Keywords

34C58F
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 3 , 01 June 1997 , pp. 582 - 599
Copyright
Copyright © Canadian Mathematical Society 1997

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