Abstract
Cosymmetries have been introduced by Yudovich and Kurakin to study limit cycles near manifolds of equilibria via Lyapunov-Schmidt reduction [49, 50]. They turn out to be equivalent to the existence of manifolds of equilibria, provided some non-degeneracy conditions are satisfied.
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References
Kurakin, L., Yudovich, V.: Bifurcation of the branching of a cycle in n-parameter family of dynamic systems with cosymmetry. Chaos 7(3), 376–386 (1997)
Kurakin, L., Yudovich, V.: Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation). Chaos 11(4), 780–794 (2001)
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Liebscher, S. (2015). Cosymmetries. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_3
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DOI: https://doi.org/10.1007/978-3-319-10777-6_3
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