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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Lyapunov coefficients for monodromic tangential singularities in Filippov vector fields

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Author(s):
Novaes, Douglas D. [1] ; Silva, Leandro A. [1]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas UNICAMP, Dept Matemat, Inst Matemat Estat & Comp Cient IMECC, Rua Sergio Buarque de Holanda, 651, Cidade Univ Zef, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Journal of Differential Equations; v. 300, p. 565-596, NOV 5 2021.
Web of Science Citations: 0
Abstract

In planar analytic vector fields, a monodromic singularity can be distinguished between a focus or a center by means of the Lyapunov coefficients, which are given in terms of the power series coefficients of the first-return map defined around the singularity. In this paper, we are interested in an analogous problem for monodromic tangential singularities of piecewise analytic vector fields Z = (Z(+), Z(-)). First, we prove that the first-return map, defined in a neighborhood of a monodromic tangential singularity, is analytic, which allows the definition of the Lyapunov coefficients. Then, as a consequence of a general property for pair of involutions, we obtain that the index of the first non-vanishing Lyapunov coefficient is always even. In addition, a general recursive formula together with a Mathematica algorithm for computing the Lyapunov coefficients is obtained. We also provide results regarding limit cycles bifurcating from monodromic tangential singularities. Several examples are analyzed. (C) 2021 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/16430-8 - Global dynamics of nonsmooth differential equations
Grantee:Douglas Duarte Novaes
Support Opportunities: Regular Research Grants