On the Chebyshev property for a new family of functions

Armengol Gasull, J. Tomás Lázaro, Joan Torregrosa

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

We analyze whether a given set of analytic functions is an Extended Chebyshev system. This family of functions appears studying the number of limit cycles bifurcating from some nonlinear vector field in the plane. Our approach is mainly based on the so called Derivation-Division algorithm. We prove that under some natural hypotheses our family is an Extended Chebyshev system and when some of them are not fulfilled then the set of functions is not necessarily an Extended Chebyshev system. One of these examples constitutes an Extended Chebyshev system with high accuracy. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)631-644
JournalJournal of Mathematical Analysis and Applications
Volume387
Issue number2
DOIs
Publication statusPublished - 15 Mar 2012

Keywords

  • Chebyshev system
  • Derivation-Division algorithm
  • Limit cycles of planar systems
  • Number of zeroes of real functions

Fingerprint Dive into the research topics of 'On the Chebyshev property for a new family of functions'. Together they form a unique fingerprint.

Cite this