This paper first summarizes the theory of quasi-periodic bifurcations for dissipative
dynamical systems. Then it presents algorithms for the computation and continuation of …

Kolmogorov–Arnold–Moser (or KAM) Theory was developed for conservative (Hamiltonian)
dynamical systems that are nearly integrable. Integrable systems in their phase space …

We consider families of dynamical systems having invariant tori that carry quasi-periodic
motions. Our interest is the persistence of such tori under small, nearly-integrable …

We give a new proof of Moser's 1967 normal-form theorem for real analytic perturbations of
vector fields possessing a reducible Diophantine invariant quasi-periodic torus. The …

We prove a discrete time analogue of Moser's normal form (1967) of real analytic
perturbations of vector fields possessing an invariant, reducible, Diophantine torus; in the …

We show that in the Gevrey topology, a d-torus flow close enough to linear with a unique
rotation vector ω is linearizable as long as ω satisfies a novel Brjuno type diophantine …

The reversible context 2 in KAM theory refers to the situation where dim Fix G< 1/2 codim T,
here Fix G is the fixed point manifold of the reversing involution G and T is the invariant torus …

In this paper, we establish a KAM-theorem about the existence of invariant tori in non-
conservative dynamical systems with finitely differentiable vector fields and multiple …

Persistence of invariant tori in a perturbed dynamical system requires two kinds of conditions
to be met. A strong non-resonance condition ensures a dense quasi-periodic orbit on both …

Invariant tori of integrable dynamical systems occur both in the dissipative and in the
conservative context, but only in the latter the tori are parameterized by phase space …