On the center conditions for analytic monodromic degenerate singularities

Jaume Giné; Jaume Llibre

doi:https://doi.org/10.1142/S0218127412503038

On the center conditions for analytic monodromic degenerate singularities

Jaume Giné, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

9 Citations (Scopus)

Abstract

In this paper, we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields and can be applied independently so that the singularity is algebraic solvable or not, or has characteristic directions or not. We remark that these are the first methods which allow to study monodromic degenerate singularities with characteristic directions. © 2012 World Scientific Publishing Company.

Original language	English
Article number	1250303
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	22
Issue number	12
DOIs	https://doi.org/10.1142/S0218127412503038
Publication status	Published - 1 Jan 2012

Keywords

Bautin method
Degenerate center
algebraically solvable
first integral

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https://doi.org/10.1142/S0218127412503038

https://ddd.uab.cat/record/150541

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abstract = "In this paper, we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields and can be applied independently so that the singularity is algebraic solvable or not, or has characteristic directions or not. We remark that these are the first methods which allow to study monodromic degenerate singularities with characteristic directions. {\textcopyright} 2012 World Scientific Publishing Company.",

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AU - Llibre, Jaume

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AB - In this paper, we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields and can be applied independently so that the singularity is algebraic solvable or not, or has characteristic directions or not. We remark that these are the first methods which allow to study monodromic degenerate singularities with characteristic directions. © 2012 World Scientific Publishing Company.

KW - Bautin method

KW - Degenerate center

KW - algebraically solvable

KW - first integral

U2 - https://doi.org/10.1142/S0218127412503038

DO - https://doi.org/10.1142/S0218127412503038

M3 - Article

SN - 0218-1274

VL - 22

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 12

M1 - 1250303

ER -

On the center conditions for analytic monodromic degenerate singularities

Abstract

Keywords

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