## Normal forms and bifurcations of some equivariant vector fields.(English)Zbl 0735.58024

The paper deals with the invariant sets and their local dynamical properties including periodic solutions for equivariant vector fields using quite general and effective (especially for solving bifurcation problems of fields in higher dimensional spaces) method of normal forms.
Motivated by J. Guckenheimer [Contemp. Math. 56, 175-184 (1986; Zbl 0616.58034)], the author studies some bifurcation problems concerning $$O(2)$$ and $$O(2)\times S^ 1$$-equivariant vector fields on $$R^ 4$$ and $$C^ 2$$ whose normal forms admit invariant subvarieties the restriction to which of such vector fields often represents bifurcation problems with known solutions.

### MSC:

 37G99 Local and nonlocal bifurcation theory for dynamical systems 37G05 Normal forms for dynamical systems 37C80 Symmetries, equivariant dynamical systems (MSC2010)

Zbl 0616.58034
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### References:

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