Title: Asymptotics and complex singularities of the Lorenz attractor

Speaker: D. Viswanath, University of Michigan

Abstract: The butterfly-shaped Lorenz attractor is a fractal set made
up of infinitely many periodic orbits.  Ever since Lorenz (1963)
introduced a system of three simple ordinary differential equations,
much of the discussion of his system and its strange attractor has
adopted a dynamical point of view. In contrast, we allow time to be a
complex variable and look upon such solutions of the Lorenz system as
analytic functions. Formal analysis gives the form and coefficients of
the complex singularities of the Lorenz system. Very precise (> 500
digits) numerical computations show that the periodic orbits of the
Lorenz system have singularities which obey that form exactly or very
nearly so. Both formal analysis and numerical computation suggest that
the mathematical analysis of the Lorenz system is a problem in
analytic function theory. (Joint work with S. Sahutoglu).
