# Further Reductions of Normal Forms for Dynamical Systems

@article{Chen2000FurtherRO, title={Further Reductions of Normal Forms for Dynamical Systems}, author={Guoting Chen and Jean Della Dora}, journal={Journal of Differential Equations}, year={2000}, volume={166}, pages={79-106} }

Abstract We propose in this paper a method for obtaining a significant refinement of normal forms for dynamical systems or vector fields, with concrete and interesting applications. We use lower order nonlinear terms in the normal form for the simplifications of higher order terms. Our approach is applicable for both the non nilpotent and the nilpotent cases. For dynamical systems of dimensions 2 and 3 we give an algorithm that leads to interesting finite order normal forms which are optimal…

## 42 Citations

### An Algorithm for Computing a New Normal Form for Dynamical Systems

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2000

A new normal form for dynamical systems or vector fields which improves the classical normal forms in the sense that it is a further reduction of the classicalnormal forms is proposed and an algorithm for an effective computation of these normal forms is given.

### Normal forms for differentiable maps near a fixed point

- MathematicsNumerical Algorithms
- 2004

A significant refinement of normal forms for differentiable maps near a fixed point is proposed, rational in the sense that if the coefficients of a map are in a field K, so is its normal form.

### Poincare' renormalized forms and regular singular points of vector fields in the plane

- Mathematics
- 2001

We discuss the local behaviour of vector fields in the plane R around a regular singular point using a special kind of reduced normal forms recently introduced, i.e. Poincaré renormalized forms [Ann.…

### Algorithmic Reduction of Poincaré–Dulac Normal Forms and Lie Algebraic Structure

- Mathematics
- 2001

The Poincaré–Dulac normal form of a given resonant system is in general nonunique; given a specific normal form, one would like to further reduce it to a simplest normal form. In this Letter we give…

### Parametric normal form classification for Eulerian and rotational non-resonant double Hopf singularities.

- Mathematics
- 2018

In this paper we provide novel results on the infinite level normal form and orbital normal form classifications of nonlinear Eulerian and rotational vector fields with two pairs of non-resonant…

### Vector potential normal form classification for completely integrable solenoidal nilpotent singularities

- MathematicsJournal of Differential Equations
- 2019

### Computation of the Simplest Normal Form and Its Application

- Engineering
- 2016

This paper presents a new computation method for obtaining a significant refinement of the simplest normal form for four dimensional nonlinear systems. The formulae are derived, which can be used to…

### Analytic normal forms and symmetries of strict feedforward control systems

- Mathematics
- 2010

This paper deals with the problem of convergence of normal forms of control systems. We identify an n‐dimensional subclass of control systems, called special strict feedforward form, shortly (SSFF),…

### Formal Poincaré-Dulac renormalization for holomorphic germs

- Mathematics
- 2010

We shall describe an alternative approach to a general renormalization procedure for formal self-maps, originally suggested by Chen-Della Dora and Wang-Zheng-Peng, giving formal normal forms simpler…

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