Bounding the number of zeros of certain Abelian integrals

F. Mañosas; J. Villadelprat

doi:10.1016/j.jde.2011.05.026

Bounding the number of zeros of certain Abelian integrals

F. Mañosas, J. Villadelprat

Departament de Matemàtiques

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In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k-1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. © 2011 Elsevier Inc.

Idioma original	Anglès
Pàgines (de-a)	1656-1669
Revista	Journal of Differential Equations
Volum	251
DOIs	https://doi.org/10.1016/j.jde.2011.05.026
Estat de la publicació	Publicada - 15 de set. 2011

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10.1016/j.jde.2011.05.026

https://ddd.uab.cat/record/150430Llicència: C In Copyright

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title = "Bounding the number of zeros of certain Abelian integrals",

abstract = "In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k-1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. {\textcopyright} 2011 Elsevier Inc.",

keywords = "Abelian integral, Chebyshev system, Hamiltonian perturbation, Limit cycle, Wronskian",

author = "F. Ma{\~n}osas and J. Villadelprat",

year = "2011",

month = sep,

day = "15",

doi = "10.1016/j.jde.2011.05.026",

language = "English",

volume = "251",

pages = "1656--1669",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Bounding the number of zeros of certain Abelian integrals

AU - Mañosas, F.

AU - Villadelprat, J.

PY - 2011/9/15

Y1 - 2011/9/15

N2 - In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k-1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. © 2011 Elsevier Inc.

AB - In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k-1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. © 2011 Elsevier Inc.

KW - Abelian integral

KW - Chebyshev system

KW - Hamiltonian perturbation

KW - Limit cycle

KW - Wronskian

U2 - 10.1016/j.jde.2011.05.026

DO - 10.1016/j.jde.2011.05.026

M3 - Article

SN - 0022-0396

VL - 251

SP - 1656

EP - 1669

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Bounding the number of zeros of certain Abelian integrals

Resum

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