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On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields

Full text
Author(s):
Santana, Paulo
Total Authors: 1
Document type: Journal article
Source: SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES; v. N/A, p. 14-pg., 2024-05-20.
Abstract

It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytic vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this paper, we prove that non-hyperbolic limit cycles of odd degree are also structurally unstable in the polynomial case, if we consider Whitney's topology. (AU)

FAPESP's process: 22/14353-1 - Study of polycycles with applications in game theory
Grantee:Paulo Henrique Reis Santana
Support Opportunities: Scholarships abroad - Research Internship - Doctorate
FAPESP's process: 21/01799-9 - The study of vector fields with applications at game theory
Grantee:Paulo Henrique Reis Santana
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants