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

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 …

Many natural and manmade dynamical systems that are modeled as large nonlinear
multioscillator systems like power systems are hard to analyze. For such systems, we …

Poincaré Normal and Renormalized Forms Page 1 Acta Applicandae Mathematicae
70: 113–131, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. 113 …

We survey and discuss Poincaré–Dulac normal forms of maps near a fixed point. The
presentation is accessible with no particular prerequisites. After some introductory material …

We present a survey of results about Poincaré–Dulac normal forms and normalizing
transformations, with emphasis on the close connection between symmetry properties and …

Lie algebras of vector fields The vector space of analytic vector fields on an open subset U of
ℂ n, with the bracket [p, q] defined by [p, q](x)≔ Dq (x) p (x)− Dp (x) q (x) becomes a Lie …

In the Landau theory of phase transitions one considers an effective potential Φ whose
symmetry group G and degree d depend on the system under consideration; generally …

We introduce an embedding of real or complex n-dimensional space Kn as an algebraic
variety V which is determined by the action of a linear one-parameter group. Every analytic …

Perturbation theory A theory aiming at studying solutions of a differential equation (or system
thereof), possibly depending on external parameters, near a known solution and/or for …