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arXiv · 1905.13169

Complex Germen on invariant isotropic tori under the Hamiltonian phases flow with in involution Hamilton functions

Amaury Alvarez Cruz·Baldomero Valiño Alonso
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Abstract

M. M. Nekhoroshev put forward the problem of to find the Complex Germ on a isotropic invariant torus with respect to Hamiltonian phases flows which come from k-functions in involution. This statement was partially solved in [9] establishing that if certain simplectic operator has a simple spectrum then the complex germ exist. In this work we solve this problem, providing a full solution, i.e. we present conditions for the existence and uniqueness of complex germ through the monodromy operator constructed in [9], but without the simple spectrum condition. We study also the Hamiltonian system with cyclic variables.

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Amaury Alvarez Cruz, Baldomero Valiño Alonso. 2019-05-13. Complex Germen on invariant isotropic tori under the Hamiltonian phases flow with in involution Hamilton functions. https://arxiv.org/abs/1905.13169

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