On the Dulac's problem for piecewise analytic vector fields

Author(s)

Andrade, K. da S. ^[1] ; Jeffrey, M. R. ^[2] ; Martins, R. M. ^[3] ; Teixeira, M. A. ^[3]

Affiliation

^[1] Univ Fed Goias, IME, Dept Math, BR-74690900 Goiania, Go - Brazil

^[2] Univ Bristol, Engn Math, Merchant Venturers Bldg, Bristol BS8 1UB, Avon - England

^[3] Univ Estadual Campinas, IMECC, Dept Math, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 266, n. 4, p. 2259-2273, FEB 5 2019.
• Web of Science Citations: 0

Abstract

This paper presents a version of Dulac's Problem for piecewise analytic vector fields that states conditions for the number of limit cycles around certain minimal sets. A suitable model-theoretic structure is introduced under which a qualitative investigation of the problem is settled. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/07523-9 - Bifurcations of Degenerated Cycles in Discontinuous Systems
• Grantee: Kamila da Silva Andrade
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 18/03338-6 - Global dynamics of piecewise smooth dynamical systems
• Grantee: Ricardo Miranda Martins
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/06903-8 - Minimal sets in non-smooth dynamical systems
• Grantee: Ricardo Miranda Martins
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/21259-5 - Typical cycles in piecewise smooth dynamical systems
• Grantee: Kamila da Silva Andrade
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate