Nonexistence of Isochronous Centers in Planar Polynomial Hamiltonian Systems of Degree Four |
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| Authors: | X JarqueJ Villadelprat |
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| Institution: | a Department d'Economia i d'Història Econòmica, Escola d'Empresarials de Sabadell, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spainb Department de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain |
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| Abstract: | In this paper we study centers of planar polynomial Hamiltonian systems and we are interested in the isochronous ones. We prove that every center of a polynomial Hamiltonian system of degree four (that is, with its homogeneous part of degree four not identically zero) is nonisochronous. The proof uses the geometric properties of the period annulus and it requires the study of the Hamiltonian systems associated to a Hamiltonian function of the form H(x, y)=A(x)+B(x) y+C(x) y2+D(x) y3. |
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