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A cohomological index of Fuller type for set-valued dynamical systems. (English) Zbl 1232.54023

F. B. Fuller [Am. J. Math. 89, 133–145 (1967; Zbl 0152.40204)] introduced an index counting the periodic orbits of a smooth vector field. Here the theory of a cohomological index of Fuller type is developed for the detection of periodic orbits of a set-valued dynamical system generated by a differential inclusion (in this setting solutions are not unique). This is used to find a general result on bifurcation of periodic orbits from an equilibrium point of a differential inclusion.

MSC:

54C60 Set-valued maps in general topology
34A60 Ordinary differential inclusions
34K18 Bifurcation theory of functional-differential equations
55N05 Čech types
37C27 Periodic orbits of vector fields and flows
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 0152.40204
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Full Text: DOI

References:

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