Unique Normal Forms for Nilpotent Planar Vector Fields
نویسندگان
چکیده
منابع مشابه
Monodromy problem for the degenerate critical points
For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...
متن کاملFurther Reductions of Normal Forms for Dynamical Systems
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 ...
متن کاملThe First Return Map for Planar Vector Fields with Nilpotent Linear Part with a Center or a Focus
The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals built with algebraic functions.
متن کاملNilpotent normal form for divergence-free vector fields and volume-preserving maps
We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in R has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. ...
متن کاملThe Problem of Distinguishing between a Center and a Focus for Nilpotent and Degenerate Analytic Systems
In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 12 شماره
صفحات -
تاریخ انتشار 2002