The Catholic University of America

Washington, DC 20064

SEMINAR IN FUNCTIONAL ANALYSIS

AND RELATED AREAS

Wednesday, November 18, 2009

4:45 - 6:30 p.m. (including a coffee-break)

SPEAKER: Michael Somos, Georgetown University

TITLE: Global behavior of an AGM-related iteration

ABSTRACT:

Iteration of the map (a,b) |--> ((a + b)/2, sqrt(ab)) yields a sequence convergent to a limit (p, p) where p is called the arithmetic-geometric mean (AGM) of a and b. The AGM goes back more than two hundred years, and was studied by Gauss and Lagrange and in nonhomogeneous form by Legendre. The map (a,b) |--> (a + b, ab) is a simpler, rational variant of the AGM map. The speaker will investigate its global behavior, periodic points, and parametrization.

PLACE: McMahon Hall, Room 209

ORGANIZERS: V. Bogdan, A. Levin and P. Saworotnow (The Catholic University of America), and P. Kainen and A. Vogt (Georgetown University)

Telephone: 202-319-5221

Fax: 202-319-5231

Email: levin@cua.edu

Webpage: http://math.cua.edu/seminar