Department of Mathematics University of Haifa COLLOQUIUM SPEAKER: Prof. Adi Ben-Israel (Rutgers University) TOPIC: Inverse Newton Transform DATE: Tuesday, January 11th 2011. TIME: 4:10 PM. (Or 4:30 PM if there is a soccer game) PLACE Room 614 on the 6th floor of the Science & Education Building (opposite the main building), University of Haifa. Abstract Let u:R-->R. A function f:R-->R is an Inverse Newton Transform of u, denoted f=INT(u), if u(x) = x - f(x)/f'(x), i.e. if the iteration x:=u(x) is identical to the Newton iteration on f(x). The INT is determined up to a constant, and is given by f(x) = exp{integral{dx/(x-u(x))}} whenever the integral exists. Some results for u and f =INT(u): (a) The fixed points of u are the zeros of f, and zeros of order > 1/2, where u is continuously differentiable, are attractive fixed points. (b) f is increasing [decreasing] if x > u(x) [< u(x)] (c) f is convex[concave] if u is differentiable and increasing[decreasing]. These results allow a new interpretation, and visualization, of chaos. The paper can be downloaded in <http://benisrael.net/Newton.html> , number 15 --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <berger@math.haifa.ac.il>