Abelian integrals and non-generic turning points

In this paper we initiate the study of the Chebyshev property of Abelian integrals generated by a non-generic turning point in planar slow-fast systems. Such Abelian integrals generalize the Abelian integrals produced by a slow-fast Hopf point (or generic turning point), introduced in Dumortier et a...

Full description

Bibliographic Details
Authors: Huzak, Renato; Rojas, David|||0000-0001-7247-4705
Format: Article
Publication date:2022
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:259951
Online Access:https://ddd.uab.cat/record/259951
https://dx.doi.org/urn:doi:10.1007/s12346-022-00609-7
Access Level:Open access
Keyword:Abelian integrals
Chebyshev systems
Planar turning points
Description
Summary:In this paper we initiate the study of the Chebyshev property of Abelian integrals generated by a non-generic turning point in planar slow-fast systems. Such Abelian integrals generalize the Abelian integrals produced by a slow-fast Hopf point (or generic turning point), introduced in Dumortier et al. (Discrete Contin Dyn Syst Ser S 2(4):723-781, 2009), and play an important role in studying the number of limit cycles born from the non-generic turning point.