On the number of critical periods for planar polynomial systems

Anna Cima; Armengol Gasull; Paulo R. da Silva

doi:https://doi.org/10.1016/j.na.2007.07.031

On the number of critical periods for planar polynomial systems

Anna Cima, Armengol Gasull, Paulo R. da Silva

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

25 Citations (Scopus)

Abstract

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree ℓ with at least 2 [(ℓ - 2) / 2] critical periods as well as study concrete families of potential, reversible and Liénard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation. © 2007 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1889-1903
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	69
DOIs	https://doi.org/10.1016/j.na.2007.07.031
Publication status	Published - 1 Oct 2008

Keywords

Critical periods
Hamiltonian centers
Liénard centers
Period function
Perturbations
Potential systems
Reversible centers

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https://doi.org/10.1016/j.na.2007.07.031

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title = "On the number of critical periods for planar polynomial systems",

abstract = "In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree ℓ with at least 2 [(ℓ - 2) / 2] critical periods as well as study concrete families of potential, reversible and Li{\'e}nard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation. {\textcopyright} 2007 Elsevier Ltd. All rights reserved.",

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T1 - On the number of critical periods for planar polynomial systems

AU - Cima, Anna

AU - Gasull, Armengol

AU - da Silva, Paulo R.

PY - 2008/10/1

Y1 - 2008/10/1

N2 - In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree ℓ with at least 2 [(ℓ - 2) / 2] critical periods as well as study concrete families of potential, reversible and Liénard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation. © 2007 Elsevier Ltd. All rights reserved.

AB - In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree ℓ with at least 2 [(ℓ - 2) / 2] critical periods as well as study concrete families of potential, reversible and Liénard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation. © 2007 Elsevier Ltd. All rights reserved.

KW - Critical periods

KW - Hamiltonian centers

KW - Liénard centers

KW - Period function

KW - Perturbations

KW - Potential systems

KW - Reversible centers

U2 - https://doi.org/10.1016/j.na.2007.07.031

DO - https://doi.org/10.1016/j.na.2007.07.031

M3 - Article

VL - 69

SP - 1889

EP - 1903

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -

On the number of critical periods for planar polynomial systems

Abstract

Keywords

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