Counting configurations of limit cycles and centers

Armengol Gasull, Antoni Guillamon, Víctor Mañosa Fernández

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We present several results on the determination of the number and distribution of limit cycles or centers for planar systems of differential equations. In most cases, the study of a recurrence is one of the key points of our approach. These results include the counting of the number of configurations of stabilities of nested limit cycles, the study of the number of different configurations of a given number of limit cycles, the proof of some quadratic lower bounds for Hilbert numbers and some questions about the number of centers for planar polynomial vector fields.
Original languageEnglish
Pages (from-to)0078-96
Number of pages19
JournalBuletinul Academiei de Stiinte a Republicii Moldova. Matematica
Volume101
Issue number1
DOIs
Publication statusPublished - 2023

Keywords

  • Limit cycle
  • Configuration
  • Center
  • Phase portrait
  • Recurrence
  • Fibonacci numbers

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