Monodromy and stability for nilpotent critical points

A. Gasull; M. J. Álvarez

doi:https://doi.org/10.1142/S0218127405012740

Monodromy and stability for nilpotent critical points

A. Gasull, M. J. Álvarez

Department of Mathematics

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

66 Citations (Scopus)

Abstract

We give a new and short proof of the characterization of monodromic nilpotent critical points. We so calculate the first generalized Lyapunov constants in order to solve the stability problem. We apply the results to several families of planar systems obtaining necessary and sufficient conditions for having a center. Our method also allows us to generate limit cycles from the origin. © World Scientific Publishing Company.

Original language	English
Pages (from-to)	1253-1265
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	15
DOIs	https://doi.org/10.1142/S0218127405012740
Publication status	Published - 1 Jan 2005

Keywords

Limit cycle
Nilpotent critical point

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Cite this

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abstract = "We give a new and short proof of the characterization of monodromic nilpotent critical points. We so calculate the first generalized Lyapunov constants in order to solve the stability problem. We apply the results to several families of planar systems obtaining necessary and sufficient conditions for having a center. Our method also allows us to generate limit cycles from the origin. {\textcopyright} World Scientific Publishing Company.",

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AU - Álvarez, M. J.

PY - 2005/1/1

Y1 - 2005/1/1

N2 - We give a new and short proof of the characterization of monodromic nilpotent critical points. We so calculate the first generalized Lyapunov constants in order to solve the stability problem. We apply the results to several families of planar systems obtaining necessary and sufficient conditions for having a center. Our method also allows us to generate limit cycles from the origin. © World Scientific Publishing Company.

AB - We give a new and short proof of the characterization of monodromic nilpotent critical points. We so calculate the first generalized Lyapunov constants in order to solve the stability problem. We apply the results to several families of planar systems obtaining necessary and sufficient conditions for having a center. Our method also allows us to generate limit cycles from the origin. © World Scientific Publishing Company.

KW - Limit cycle

KW - Nilpotent critical point

U2 - https://doi.org/10.1142/S0218127405012740

DO - https://doi.org/10.1142/S0218127405012740

M3 - Article

VL - 15

SP - 1253

EP - 1265

ER -

Monodromy and stability for nilpotent critical points

Abstract

Keywords

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