Stability conditions for reversible and partially integrable systems

• Autor(a) principal: Buzzi, Claudio A. [UNESP]
• Data de Publicação: 2021
• Outros Autores: Roberto, Luci Any F. [UNESP], Teixeira, Marco A.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.4171/PM/2060; http://hdl.handle.net/11449/223389
• topic: integrability; Peixoto’s Theorem; reversible systems; Structural stability

The purpose of this paper is to provide results like Peixoto’s Theorem inside a class (Formula presented) of 3-dimensional reversible systems. We deal with reversible systems associated to an involution φ1 such that Dim Fix(φ1) is equal to one. We further assume the existence of a first integral for any X ∈ (Formula presented) that leaves invariant any sphere centered at the origin. The main result establishes generic necessary conditions for the structural stability in (Formula presented). Stability conditions on generic one-parameter families of reversible vector fields on the two-dimensional sphere are also stated.