Stability conditions for reversible and partially integrable systems
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European Mathematical Society - EMS - Publishing House
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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.
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Portugaliae Mathematica, v. 78, n. 1, p. 43-63, 2021.
