| Popis: |
We study the problem of the existence and of the geometric structure of the set of periodic orbits of a vector field in presence of a first integral. We give a unified treatment and a geometric proof of existence results of periodic orbits by Moser (local case) and Bottkol (global case) under a suitable nonresonance condition. The local resonance case is considered, too. For analytic vector fields admitting an analytic first integral, we give a geometric description of the set of periodic orbits, proving that it is an analytic set, hence extending a theorem by Siegel. |
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