The purpose of this paper is to provide results like Peixotos Theorem inside a class of 3-dimensional reversible systems. We deal with reversible systems associated to an involution such that is equal to one. We further assume the existence of a first integral for any that leaves invariant any sphere centered at the origin. The main result establishes generic necessary conditions for the structural stability in . Stability conditions on generic one-parameter families of reversible vector fields on the two-dimensional sphere are also stated.
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Claudio A. Buzzi, Luci Any F. Roberto, Marco A. Teixeira, Stability conditions for reversible and partially integrable systems. Port. Math. 78 (2021), no. 1, pp. 43–63DOI 10.4171/PM/2060