Stability conditions for reversible and partially integrable systems

  • Claudio A. Buzzi

    UNESP - São Paulo State University, Brazil
  • Luci Any F. Roberto

    UNESP - São Paulo State University, Brazil
  • Marco A. Teixeira

    UNICAMP Universidade Estadual de Campinas, São Paulo, Brazil
Stability conditions for reversible and partially integrable systems cover

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Abstract

The purpose of this paper is to provide results like Peixoto’s 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.

Cite this article

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. 43–63

DOI 10.4171/PM/2060