# Finite determinacy of matrices

Speaker
Dmitry Kerner (BGU)
Date
14/12/2014 - 13:00 - 12:00Add to Calendar 2014-12-14 12:00:00 2014-12-14 13:00:00 Finite determinacy of matrices Let f be a power series (in several variables) or a C^\infty-smooth function. In many cases just a finite part of Taylor expansion is enough to determine f up to the change of coordinates. Alternatively, the deformations of f by terms of high enough orders are trivial. This phenomenon is called the finite determinacy.  An immediate application is the algebraization: f has a polynomial representative. More generally, for maps of smooth spaces the finite determinacy (under various group-actions) has been intensively studied for about 50 years (by Mather, Tougeron, Arnol'd, Wall and many others).   אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

Let f be a power series (in several variables) or a C^\infty-smooth function. In many cases just a finite part of Taylor expansion is enough to determine f up to the change of coordinates. Alternatively, the deformations of f by terms of high enough orders are trivial. This phenomenon is called the finite determinacy.
An immediate application is the algebraization: f has a polynomial representative.

More generally, for maps of smooth spaces the finite determinacy (under various group-actions) has been intensively studied for about 50 years (by Mather, Tougeron, Arnol'd, Wall and many others).

תאריך עדכון אחרון : 09/12/2014