Related papers: Poincare' normal and renormalized forms
In this revised version, applying a general renormalization procedure for formal self-maps, producing a formal normal form simpler than the classical Poincar\'e-Dulac normal form, we shall give a complete list of normal forms for…
The Poincare'-Dulac normal form of a given resonant system is in general non unique; given a specific normal form, one would like to further reduce it to a simplest normal form. In this note we give an algorithm, based on the Lie algebraic…
We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and…
We discuss the convergence problem for coordinate transformations which take a given vector field into Poincar\'e-Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guaranteee convergence of these…
We present a geometric proof of the Poincar\'e-Dulac Normalization Theorem for analytic vector fields with singularities of Poincar\'e type. Our approach allows us to relate the size of the convergence domain of the linearizing…
In this article, we develop a new approach to the Poincar\'e--Dulac normal form theory for a system of differential equations near a singular point. Using the continuous averaging method, we construct a normalization flow that moves a…
We discuss the local behaviour of vector fields in the plane $\R^2$ around a regular singular point, using recently introduced reduced normal forms, i.e. Poincar\'e and Lie renormalized forms [{\it Lett. Math. Phys.} {\bf 42} (1997),…
We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a self-contain introduction to the mould…
The general term of the Poincare normalizing series is explicitly constructed for non-resonant systems of ODE's in a large class of equations. In the resonant case, a non-local transformation is found, which exactly linearizes the ODE's and…
We show that a nonlinear dynamical system in Poincare'-Dulac normal form (in $\R^n$) can be seen as a constrained linear system; the constraints are given by the resonance conditions satisfied by the spectrum of (the linear part of) the…
There are two ways to compute Poincar\'e-Dulac normal forms of systems of ODEs. Under the original approach used by Poincar\'e the normalizing transformation is explicitly computed. On each step, the normalizing procedure requires the…
We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and…
We examine deformed Poincar\'e algebras containing the exact Lorentz algebra. We impose constraints which are necessary for defining field theories on these algebras and we present simple field theoretical examples. Of particular interest…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
We discuss several aspects of the geometry of vector fields in (Poincare'-Dulac) normal form. Our discussion relies substantially on Michel theory and aims at a constructive approach to simplify the analysis of normal forms via a splitting…
We study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal)…
Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…
We introduce Poincar\'e type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.
We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.
We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincare-Dulac normal form, and the convergence of such transformations. We first review A.D. Bruno's approach to formal normalization, as…