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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.