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Journal of Dynamical and Control Systems

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05-10-2017

On First Integrals for Holomorphic Vector Fields

Author: Jonny Ardila

Published in: Journal of Dynamical and Control Systems | Issue 3/2018

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Abstract

It is proven that a generic vector field in \(\mathbb {C}^{3}\) having a formal first integral or non-enumerable many invariant hypersurfaces and closed leaves off the singularity has a holomorphic first integral.

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Anosov D, Dawson E, OShea D, Arnold V, Aranson S, Bronshtein I, Grines V, Ilyashenko Y. Dynamical systems I: ordinary differential equations and smooth dynamical systems. Problem Books in Mathematics. Berlin: Springer; 1996. ISBN 9783540612209. https://books.google.com.co/books?id=ZSQgqwlPsmkC.

Arnol′d VI. Ordinary differential equations, 3rd ed. New York: Springer Textbook; 1992. Translated from the Russian by Roger Cooke.

Brochero Martínez FE. Groups of germs of analytic diffeomorphisms in \((\mathbb {C}^{2},0)\). J Dynam Control Systems 2003;9(1):1–32. https://doi.org/10.1023/A:1022101132569.MathSciNetCrossRefMATH

Câmara L, Scárdua B. On the integrability of holomorphic vector fields. Discrete Contin Dyn Syst 2009;25(2):481–493. https://doi.org/10.3934/dcds.2009.25.481.MathSciNetCrossRefMATH

Cerveau D, Lins Neto A. Frobenius theorem for foliations on singular varieties. Bull Braz Math Soc (N.S.) 2008;39(3):447–469. https://doi.org/10.1007/s00574-008-0016-2.MathSciNetCrossRefMATH

Darboux G. Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré. Bulletin des Sciences Mathé,matiques et Astronomiques 1878;2(1):151–200.MATH

Elizarov PM, Il′yashenko YS. Remarks on orbital analytic classification of germs of vector fields. Mat Sb (N.S.) 1983;121(163)(1):111–126.MathSciNet

Gunning RC. Introduction to holomorphic functions of several variables. Vol. I. The Wadsworth & Brooks/Cole Mathematics Series. Pacific Grove: Wadsworth & Brooks/Cole Advanced Books & Software; 1990. Function theory.

Gunning RC. Introduction to holomorphic functions of several variables. Vol. II. The Wadsworth & Brooks/Cole Mathematics Series. Monterey: Wadsworth & Brooks/Cole Advanced Books & Software; 1990. Local theory.

10.

Jouanolou J-P. Équations de Pfaff alègbriques. Lecture notes in Mathematics, 1st ed. Berlin: Springer; 1979. ISBN 9783540092391,3540092390.

11.

Malgrange B. Frobenius avec singularités. I Codimension un Inst Hautes Études Sci Publ Math. 1976;46:163–173.CrossRefMATH

12.

Martelo M, Ribón J. Derived length of solvable groups of local diffeomorphisms. Math Ann 2014;358(3–4):701–728. https://doi.org/10.1007/s00208-013-0975-5.MathSciNetCrossRefMATH

13.

Martelo M, Scárdua B. Integrating factors for groups of formal complex diffeomorphisms. J Dyn Control Syst 2013;19(2):195–235. https://doi.org/10.1007/s10883-013-9170-y.MathSciNetCrossRefMATH

14.

Mattei J-F, Moussu R. Holonomie et intégrales premières. Ann Sci École Norm Sup (4) 1980;13(4):469–523. http://www.numdam.org/item?id=ASENS_1980_4_13_4_469_0.MathSciNetCrossRefMATH

15.

Reis H. Equivalence and semi-completude of foliations. Nonlinear Anal 2006;64(8):1654–1665. https://doi.org/10.1016/j.na.2005.07.013.MathSciNetCrossRefMATH

16.

Ribón J. The solvable length of groups of local diffeomorphisms. 2014. arXiv:1406.0902R.

17.

Ribón J. Algebraic properties of groups of complex analytic local diffeomorphisms VIII Escuela doctoral intercontinental de matemáticas. 2015.

Title: On First Integrals for Holomorphic Vector Fields
Author: Jonny Ardila
Publication date: 05-10-2017
Publisher: Springer US
Published in: Journal of Dynamical and Control Systems / Issue 3/2018
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-017-9385-4

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