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KAM Tori and Quantum Birkhoff Normal Forms

Georgi Popov (1999/2000)

Séminaire Équations aux dérivées partielles

This talk is concerned with the Kolmogorov-Arnold-Moser (KAM) theorem in Gevrey classes for analytic hamiltonians, the effective stability around the corresponding KAM tori, and the semi-classical asymptotics for Schrödinger operators with exponentially small error terms. Given a real analytic Hamiltonian H close to a completely integrable one and a suitable Cantor set Θ defined by a Diophantine condition, we find a family Λ ω , ω Θ , of KAM invariant tori of H with frequencies ω Θ which is Gevrey smooth with...

Killing spinor-valued forms and the cone construction

Petr Somberg, Petr Zima (2016)

Archivum Mathematicum

On a pseudo-Riemannian manifold 𝕄 we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on 𝕄 and parallel fields on the metric cone over 𝕄 for spinor-valued forms.

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