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Keeping track of limit cycles. (English) Zbl 0602.34019
We give a solution to Hilbert’s 16th problem when an a priori bound on the period is imposed. Also, we give an upper bound on the arclength which generalizes a previous convexity statement for quadratic vector fields. We use a theorem on subanalytic sets and methods of differential analysis.

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
32B20 Semi-analytic sets, subanalytic sets, and generalizations
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