Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as
phase spaces. They also arise naturally in other mathematical problems, and form a bridge …

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to
describe the recent progress in nonlinear differential equations and nonlinear dynamical …

Vibration problems are naturally formulated with second-order equations of motion. When
the vibration problem is nonlinear in nature, using normal form analysis currently requires …

We show that a holomorphic vector field in a neighbourhood of its singular point 0∈ C n is
analytically normalizable if it has a sufficiently large number of commuting holomorphic …

We show that, to find a Poincare-Dulac normalization for a vector field is the same as to find
and linearize a torus action which preserves the vector field. Using this toric characterization …

This is a survey on natural local torus actions which arise in integrable dynamical systems,
and their relations with other subjects, including: reduced integrability, local normal forms …

The concept of unique normal form is formulated in terms of a spectral sequence. As an
illustration of this technique some results of Baider and Churchill concerning the normal form …

In Poincare Normal Form theory, one considers a series of transformations generated by
homogeneous polynomials obtained as solution of the homological equation; such solutions …

We discuss the convergence problem for coordinate transformations which take a given
vector field into Poincaré–Dulac normal form. We show that the presence of linear or …

This paper concerns perturbations of smooth vector fields on. Finally, the exceptional sets
associated with the simultaneous Diophantine conditions are studied. A generalized …