Autor(es)

Carvalho, Tiago ; Cunha, Jackson ; Perez, Otavio Henrique

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 453, p. 36-pg., 2025-11-03.

Resumo

In this paper we are dealing with planar piecewise smooth vector fields defined in two zones. In each one of such zones takes place a smooth vector field and the switching manifold is a curve passing through the origin. The first one of these smooth vector fields has a saddle-node equilibrium at the origin, while the second one is transversal to the switching manifold at the origin. We will consider a singular perturbation of this scenario, involving a non-hyperbolic equilibrium considered over the switching manifold. With this purpose, we regularize the piecewise smooth vector field using the Sotomayor-Teixeira method. After it, the singular perturbation theory is considered and a unique non-normally hyperbolic point is obtained and a sequence of blow-ups is considered in order to completely desingularize this point and understand the dynamics around it. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU)

• Processo FAPESP: 22/02819-6 - Sistemas dinâmicos via campos vetoriais intermitentes: aspectos teóricos e aplicações
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Projeto Inicial
• Processo FAPESP: 21/10198-9 - Variedades invariantes e conjuntos periódicos limite de folheações descontínuas
• Beneficiário: Otavio Henrique Perez
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 21/12395-6 - Campos vetoriais suaves por partes: aspectos teóricos e aplicações
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular