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math.DS2023
Singular KAM Theory
Luca Biasco, Luigi Chierchia
The question of the total measure of invariant tori in analytic, nearly--integrable Hamiltonian systems is considered. In 1985, Arnol'd, Kozlov and Neishtadt, in the Encyclopaedia…
math.DS2023
Global properties of generic real-analytic nearly-integrable Hamiltonian systems
Luca Biasco, Luigi Chierchia
We introduce a new class of generic real analytic potentials on and study global analytic properties of natural nearly-integrable Hamiltonians $\fra…
math.DS2023
Complex Arnol'd-Liouville maps
Luca Biasco, Luigi Chierchia
We discuss the holomorphic properties of the complex continuation of the classical Arnol'd-Liouville action-angle variables for real analytic 1 degree--of--freedom Hamiltonian syst…