Monodromy and stability for nilpotent critical points

A. Gasull, M. J. Álvarez

Research output: Contribution to journalArticleResearchpeer-review

66 Citations (Scopus)


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 languageEnglish
Pages (from-to)1253-1265
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Publication statusPublished - 1 Jan 2005


  • Limit cycle
  • Nilpotent critical point


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