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On the period function of planar systems with unknown normalizers


Author: M. Sabatini
Journal: Proc. Amer. Math. Soc. 134 (2006), 531-539
MSC (2000): Primary 34C05
DOI: https://doi.org/10.1090/S0002-9939-05-08032-9
Published electronically: July 21, 2005
MathSciNet review: 2176022
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Abstract: A necessary and sufficient condition for the period function's monotonicity on a period annulus is given. The approach is based on the theory of normalizers, but is applicable without actually knowing a normalizer. Some applications to polynomial and Hamiltonian systems are presented.


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Additional Information

M. Sabatini
Affiliation: Department of Mathematics, University of Trento, via Sommarive 14, I-38050, Povo, Italy

DOI: https://doi.org/10.1090/S0002-9939-05-08032-9
Keywords: Normalizer, period annulus, Hamiltonian system
Received by editor(s): June 25, 2004
Received by editor(s) in revised form: July 8, 2004, and September 29, 2004
Published electronically: July 21, 2005
Additional Notes: This work was partially supported by the COFIN group \lq\lq Equazioni differenziali ordinarie e applicazioni", and by the intergroup project \lq\lq Dinamica anolonoma, perturbazioni e orbite periodiche".
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society

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