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Numeric invariants in semilocal bifurcations. (English) Zbl 1464.37030

Summary: Bifurcations that occur in a small neighborhood of a polycycle of a planar vector field are called semilocal. We prove that even semilocal bifurcations of hyperbolic polycycles may have numeric invariants of topological classification.

MSC:

37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37G05 Normal forms for dynamical systems
37G10 Bifurcations of singular points in dynamical systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
47J15 Abstract bifurcation theory involving nonlinear operators
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References:

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