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The Weinstein conjecture in \(P\times {\mathbb{C}}^{\ell}\). (English) Zbl 0666.58019

Using first order systems we show that every Hamiltonian system in \(P\times {\mathbb{C}}^{\ell}\) has a periodic solution near any prescribed compact regular energy surface. This result implies in particular the Weinstein conjecture in \(P\times {\mathbb{C}}^{\ell}\).
Reviewer: A.Floer

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58E30 Variational principles in infinite-dimensional spaces
34C25 Periodic solutions to ordinary differential equations
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