Bifurcations of Zeros in Translated Families of Functions and Applications

P. Mardešić*, D. Marín, J. Villadelprat

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper, we study the creation of zeros in a certain type of families of functions. The families studied are given by the difference of two basic functions with a translation made in the argument of one of these functions. The problem is motivated by applications in the 16th Hilbert problem and its ramifications. Here, we apply the results obtained to the study of bifurcations of critical periods in the Loud family of quadratic centers.

Original languageAmerican English
JournalJournal of Dynamical and Control Systems
DOIs
Publication statusAccepted in press - 2020

Keywords

  • Bifurcations
  • Centers
  • Critical period
  • Cyclicity

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