Invariant tori, effective stability, and quasimodes with exponentially small error terms. I: Birkoff normal forms

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (34)

Gevrey-smoothness of elliptic lower dimensional invariant tori in Hamiltonian systems ⋮ Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ QUASI-INVARIANT TORI AND SEMI-EXCITED STATES FOR SCHRO¨DINGER OPERATORS. I. ASYMPTOTICS ⋮ Invariant tori for Gevrey-smooth Hamiltonian systems under Rüssmann's nondegeneracy condition ⋮ Partial preservation of frequencies and Floquet exponents in KAM theory ⋮ Nekhoroshev and KAM stabilities in generalized Hamiltonian systems ⋮ Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Rüssmann's non-degeneracy condition ⋮ The geometry of the semiclassical wave front set for Schrödinger eigenfunctions on the torus ⋮ Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann's non-degeneracy condition ⋮ Quantum ergodicity of random orthonormal bases of spaces of high dimension ⋮ Generic KAM Hamiltonians are not quantum ergodic ⋮ KAM tori are no more than sticky ⋮ Convergence of a quantum normal form and an exact quantization formula ⋮ Gevrey regularity of invariant curves of analytic reversible mappings ⋮ Positive measure of effective quasi-periodic motion near a Diophantine torus ⋮ Spectral stability and semiclassical measures for renormalized KAM systems ⋮ Local wave numbers on an n-spheres ⋮ Smooth Gevrey normal forms of vector fields near a fixed point ⋮ Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields ⋮ A new method for measuring the splitting of invariant manifolds ⋮ Gevrey smoothness of families of invariant curves for analytic area preserving mappings ⋮ Gevrey-smoothness of lower dimensional hyperbolic invariant tori for nearly integrable symplectic mappings ⋮ Invariant hyperbolic tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition ⋮ Spectral monodromy of non-self-adjoint operators ⋮ Spaces of anisotropic ultradifferentiable functions and local solvability for semilinear partial differential equations ⋮ Quantum singular complete integrability ⋮ Rigidity of reducibility of Gevrey quasi-periodic cocycles on $U(n)$ ⋮ Schrödinger spectra and the effective Hamiltonian of weak KAM theory on the flat torus ⋮ Generic super-exponential stability of invariant tori in Hamiltonian systems ⋮ A note on Gevrey regular KAM theory and the inverse approximation lemma ⋮ A local quantum version of the Kolmogorov theorem ⋮ Gevrey estimates for asymptotic expansions of Tori in weakly dissipative systems* ⋮ Schrödinger dynamics and optimal transport of measures ⋮ On the stable eigenvalues of perturbed anharmonic oscillators in dimension two

This page was built for publication: Invariant tori, effective stability, and quasimodes with exponentially small error terms. I: Birkoff normal forms