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A Chebyshev criterion for Abelian integrals
Author(s):
M.
Grau;
F.
Mañosas;
J.
Villadelprat
Journal:
Trans. Amer. Math. Soc.
363
(2011),
109-129.
MSC (2010):
Primary 34C08, 41A50;
Secondary 34C23
Posted:
August 27, 2010
MathSciNet review:
2719674
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Abstract:
We present a criterion that provides an easy sufficient condition in order for a collection of Abelian integrals to have the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, several known results are obtained in a shorter way and some new results, which could not be tackled by the known standard methods, can also be deduced.
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Additional Information:
M.
Grau
Affiliation:
Departament de Matemàtica, Universitat de Lleida, Lleida, Spain
Email:
mtgrau@matematica.udl.cat
F.
Mañosas
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain
Email:
Francesc.Manosas@uab.cat
J.
Villadelprat
Affiliation:
Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain
Email:
Jordi.Villadelprat@urv.cat
DOI:
10.1090/S0002-9947-2010-05007-X
PII:
S 0002-9947(2010)05007-X
Keywords:
Planar vector field,
Hamiltonian perturbation,
limit cycle,
Chebyshev system,
Abelian integral
Received by editor(s):
July 3, 2008
Posted:
August 27, 2010
Additional Notes:
The first author was partially supported by the MEC/FEDER grant MTM2005-06098-C02-02. The second author was supported by the MEC/FEDER grants MTM2005-02139 and MTM2005-06098 and the CIRIT grant 2005SGR-00550. The third author was supported by the MEC/FEDER grant MTM2005-06098-C02-01 and the CIRIT grant 2005SGR-00550.
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Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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