kam Theory: quasi-periodicity in dynamical systems
HW Broer, MB Sevryuk - Handbook of dynamical systems, 2010 - Elsevier
Kolmogorov–Arnold–Moser (or KAM) Theory was developed for conservative (Hamiltonian)
dynamical systems that are nearly integrable. Integrable systems in their phase space …
dynamical systems that are nearly integrable. Integrable systems in their phase space …
[PDF][PDF] The classical KAM theory at the dawn of the twenty-first century
MB Sevryuk - Moscow Mathematical Journal, 2003 - scholar.archive.org
We survey several recent achievements in KAM theory. The achievements chosen pertain to
Hamiltonian systems only and are closely connected with the content of Kolmogorov's …
Hamiltonian systems only and are closely connected with the content of Kolmogorov's …
Partial preservation of frequencies and Floquet exponents in KAM theory
MB Sevryuk - Proceedings of the Steklov Institute of Mathematics, 2007 - Springer
Under a small perturbation of a completely integrable Hamiltonian system, invariant tori with
Diophantine frequencies of motion are not destroyed but only slightly deformed, provided …
Diophantine frequencies of motion are not destroyed but only slightly deformed, provided …
Whitney smooth families of invariant tori within the reversible context 2 of KAM theory
MB Sevryuk - Regular and Chaotic Dynamics, 2016 - Springer
We prove a general theorem on the persistence of Whitney C∞-smooth families of invariant
tori in the reversible context 2 of KAM theory. This context refers to the situation where dim …
tori in the reversible context 2 of KAM theory. This context refers to the situation where dim …
Herman's approach to quasi-periodic perturbations in the reversible KAM context 2
MB Sevryuk - arxiv preprint arxiv:1612.07653, 2016 - arxiv.org
We revisit non-autonomous systems depending quasi-periodically in time within the
reversible context 2 of KAM theory and obtain Whitney smooth families of invariant tori in …
reversible context 2 of KAM theory and obtain Whitney smooth families of invariant tori in …
Theorem on perturbation of coisotropic invariant tori of locally Hamiltonian systems and its applications
We study the problem of perturbations of quasiperiodic motions on coisotropic invariant tori
in a class of locally Hamiltonian systems. We prove a general KAM-theorem on the …
in a class of locally Hamiltonian systems. We prove a general KAM-theorem on the …
Bifurcation of coisotropic invariant tori under locally Hamiltonian perturbations of integrable systems and nondegenerate deformation of symplectic structure
We study the bifurcation problem for a Cantor set of coisotropic invariant tori in the case
where a Liouville-integrable Hamiltonian system undergoes locally Hamiltonian …
where a Liouville-integrable Hamiltonian system undergoes locally Hamiltonian …