Gevrey Normal Form and Effective Stability of Lagrangian Tori
Todor Mitev, Georgi Popov
TL;DR
This paper develops a Gevrey symplectic normal form for Hamiltonians near Lagrangian tori with Diophantine frequencies, demonstrating effective stability of quasi-periodic motions in this setting.
Contribution
It introduces a Gevrey symplectic normal form for Hamiltonians near Lagrangian tori, extending previous results to Gevrey smooth cases.
Findings
Normal form established for Gevrey smooth Hamiltonians
Effective stability of quasi-periodic motions proven
Applicable to Hamiltonians with Diophantine frequency vectors
Abstract
A Gevrey symplectic normal form of an analytic and more generally Gevrey smooth Hamiltonian near a Lagrangian invariant torus with a Diophantine vector of rotation is obtained. The normal form implies effective stability of the quasi-periodic motion near the torus.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Geometric and Algebraic Topology · Nonlinear Waves and Solitons