Big denominators and analytic normal forms

Analytic Normal Forms and Symmetries of Strict Feedforward Control Systems

Follow this and additional works at: http://opensiuc.lib.siu.edu/math_articles This is a preprint (prior to peer review) of the article published as Tall, I. A., & Respondek, W. (2009). Analytic normal forms and symmetries of strict feedforward control systems. International Journal of Robust and Nonlinear Control. doi: 10.1002/rnc.1505. The definitive version is available at http://onlinelibra...

Robust normal forms for saddles of analytic vector fields

The aim of this paper is to introduce a technique for describing trajectories of systems of ordinary differential equations (ODEs) passing near saddle-fixed points. In contrast to classical linearization techniques, the methods of this paper allow for perturbations of the underlying vector fields. This robustness is vital when modelling systems containing small uncertainties, and in the develop...

On the convergence of normal forms for analytic control systems

A fruitful technique for the local analysis of a dynamical system consists of using a local change of coordinates to transform the system to a simpler form, which is called a normal form. The qualitative behavior of the original system is equivalent to that of its normal form which may be easier to analyze. A bifurcation of a parameterized dynamics occurs when a change in the parameter leads to...

Smooth and Analytic Normal Forms: A Special Class of Strict Feedforward Forms

Normal Forms of Analytic Perturbations of Quasihomogeneous Vector Fields: Rigidity, Invariant Analytic Sets and Exponentially Small Approximation