In this monograph we introduce a new method to study bifurcations of KAM tori with fixed
Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on …

We investigate the dynamics of various problems defined by Hamiltonian systems of two and
three degrees of freedom that have in common that they can be reduced by an axial …

We consider a multi-scale, nearly integrable Hamiltonian system. With proper degeneracy
involved, such a Hamiltonian system arises naturally in problems of celestial mechanics …

In this paper, we study Kolmogorov type theorems for small perturbations of certain
degenerate Hamiltonian systems, indexed by a parameter $\xi $, with $ H (y …

This paper is a continuation to our work (Xu et al. in Ann Henri Poincaré 18 (1): 53–83,
2017) concerning the persistence of lower-dimensional tori on resonant surfaces of a multi …

In this paper, we study the persistence of invariant tori in nearly integrable multiscale
Hamiltonian systems with highorder degeneracy in the integrable part. Such Hamiltonian …

Theorems on the existence of invariant KAM tori are established for perturbations of
Hamiltonian systems which are circle bundle flows. By averaging the perturbation over the …

We consider the motion of an infinitesimal mass under the Newtonian attraction of N point
masses forming a ring plus a central body where a Manev potential (-1/r+ e/r 2, e∈ R), is …

We deal with Hamiltonian bifurcations associated with the reversible umbilic in two degrees
of freedom systems defined by 0: 1 resonance, ie the unperturbed equilibrium has two …

We consider a family of perturbed Hamiltonian systems with Hamiltonian in 1: 1: 2
resonance, where is a polynomial which is axially symmetric with respect to the-axis. Here …