On the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem Export

@article{citeulike:5695540, abstract = {We prove that the number of limit cycles generated by a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing tangential Hilbert 16th problem. The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection (Gauss-Manin connection) with a quasiunipotent monodromy group.}, archivePrefix = {arXiv}, author = {Binyamini, Gal and Novikov, Dmitry and Yakovenko, Sergei}, citeulike-article-id = {5695540}, citeulike-linkout-0 = {http://arxiv.org/abs/0808.2952}, citeulike-linkout-1 = {http://arxiv.org/pdf/0808.2952}, day = {25}, eprint = {0808.2952}, keywords = {abelian\_integrals, complex\_analysis, integrability, linear\_systems}, month = {Nov}, posted-at = {2009-09-01 07:16:43}, priority = {0}, title = {On the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem}, url = {http://arxiv.org/abs/0808.2952}, year = {2008} }

TY - JOUR ID - citeulike:5695540 L3 - citeulike-article-id:5695540 N2 - We prove that the number of limit cycles generated by a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing tangential Hilbert 16th problem. The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection (Gauss-Manin connection) with a quasiunipotent monodromy group. TI - On the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem KW - abelian_integrals KW - complex_analysis KW - integrability KW - linear_systems AU - Binyamini, Gal AU - Novikov, Dmitry AU - Yakovenko, Sergei PY - 2008/Nov/25/ UR - http://arxiv.org/abs/0808.2952 ER -