The center problem for Z2-symmetric nilpotent vector fields

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Inverse Spectral Problem for Analytic Domains Ii: Z2- Symmetric Domains

This paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit. The algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary, and on a Feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral. The algorith...

Vector Fields and Nilpotent Lie Algebras

In other words, we want to write the corresponding trajectory t → x(t) in closed form. Of course, since this cannot be done for most differential equations, it is important to find a means of approximating a general flow by a flow which is explicitly integrable in closed form. In this paper we describe an infinite dimensional family of explicitly integrable flows E; in a companion paper [6] we ...

Bi-center problem for some classes of Z2-equivariant systems

We investigate the simultaneous existence of two centers (bi-center) for two families of planar Z2-equivariant differential systems. First we present necessary and sufficient conditions for the existence of an isochronous bi-center for a planar Z2-equivariant cubic system having two centers at the points (−1, 0) and (1, 0), completing the study done by Liu and Li (2011). Next, we give condition...

Unique Normal Forms for Nilpotent Planar Vector Fields