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1996 The period function of some polynomial systems of arbitrary degree
C. B. Collins
Differential Integral Equations 9(2): 251-266 (1996). DOI: 10.57262/die/1367603345


We consider certain vector fields in the plane which possess a centre. The main result is that for Hamiltonian polynomial systems which are of even degree, which possess homogeneous nonlinearities, and which have a centre located at the origin, the period function is a strictly increasing function of the energy, throughout its interval of definition. It is also shown that for nonlinear homogeneous Hamiltonian polynomial vector fields of arbitrary degree which possess a centre, the period function is a strictly decreasing function of the energy. With appropriate modifications, this result is extended to arbitrary homogeneous vector fields which possess a centre, irrespective of their being Hamiltonian or polynomial; the period function is then strictly monotonic, except when the degree of homogeneity is one, when the systems are isochronous.


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C. B. Collins. "The period function of some polynomial systems of arbitrary degree." Differential Integral Equations 9 (2) 251 - 266, 1996.


Published: 1996
First available in Project Euclid: 3 May 2013

zbMATH: 0849.34025
MathSciNet: MR1364047
Digital Object Identifier: 10.57262/die/1367603345

Primary: 34C05
Secondary: 58F21 , 70H05

Rights: Copyright © 1996 Khayyam Publishing, Inc.


Vol.9 • No. 2 • 1996
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