We propose a version of the Poincaré-Birkhoff theorem for infinite-dimensional Hamiltonian systems, which extends a recent result by Fonda and Ureña. The twist condition, adapted to a Hilbert cube, is spread on a sequence of approximating finite-dimensional systems. Some applications are proposed to pendulum-like systems of infinitely many ODEs. We also extend to the infinite-dimensional setting a celebrated theorem by Conley and Zehnder.

An infinite-dimensional version of the Poincaré-Birkhoff theorem on the Hilbert cube

BOSCAGGIN, ALBERTO;Alessandro Fonda
;
Maurizio Garrione
2020-01-01

Abstract

We propose a version of the Poincaré-Birkhoff theorem for infinite-dimensional Hamiltonian systems, which extends a recent result by Fonda and Ureña. The twist condition, adapted to a Hilbert cube, is spread on a sequence of approximating finite-dimensional systems. Some applications are proposed to pendulum-like systems of infinitely many ODEs. We also extend to the infinite-dimensional setting a celebrated theorem by Conley and Zehnder.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2939596
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