On the number of zeros of Abelian integrals

Abstract We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in 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...
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Autor*in:	Binyamini, Gal [verfasserIn] Novikov, Dmitry Yakovenko, Sergei

Format:	Artikel
Sprache:	Englisch

Erschienen:	2010

Systematik:	SA 5940 SA 5940

Anmerkung:	© Springer-Verlag 2010

Übergeordnetes Werk:	Enthalten in: Inventiones mathematicae - Springer-Verlag, 1966, 181(2010), 2 vom: 15. Apr., Seite 227-289
Übergeordnetes Werk:	volume:181 ; year:2010 ; number:2 ; day:15 ; month:04 ; pages:227-289

Links:	Volltext

DOI / URN:	10.1007/s00222-010-0244-0

Katalog-ID:	OLC2050922906

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520			\|a Abstract We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in 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 infinitesimal 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 defined over ℚ (the Gauss-Manin connection) with a quasiunipotent monodromy group.
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author_browse	Binyamini, Gal Novikov, Dmitry Yakovenko, Sergei
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author-letter	Binyamini, Gal
doi_str_mv	10.1007/s00222-010-0244-0
dewey-full	510
title_sort	on the number of zeros of abelian integrals
title_auth	On the number of zeros of Abelian integrals
abstract	Abstract We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in 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 infinitesimal 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 defined over ℚ (the Gauss-Manin connection) with a quasiunipotent monodromy group. © Springer-Verlag 2010
abstractGer	Abstract We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in 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 infinitesimal 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 defined over ℚ (the Gauss-Manin connection) with a quasiunipotent monodromy group. © Springer-Verlag 2010
abstract_unstemmed	Abstract We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in 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 infinitesimal 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 defined over ℚ (the Gauss-Manin connection) with a quasiunipotent monodromy group. © Springer-Verlag 2010
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title_short	On the number of zeros of Abelian integrals
url	https://doi.org/10.1007/s00222-010-0244-0
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author2	Novikov, Dmitry Yakovenko, Sergei
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doi_str	10.1007/s00222-010-0244-0
up_date	2024-07-04T03:10:25.443Z
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