3:30 p.m., Friday
Dr. Florin Diacu
Department of Mathematics and Statistics
University of Victoria
The Anisotropic Manev Problem
We consider the Manev potential, given by the sum between the inverse
and the inverse square of the distance, in an anisotropic space, i.e.
such that the force acts differently in each direction. Using McGehee
coordinates, we blow up the collision singularity, paste a collision
manifold to the phase space, study the flow on and near the collision
manifold, and find a positive-measure set of collision orbits. Besides
frontal homothetic, frontal nonhomothetic, and spiraling
collisions and ejections, we put into the evidence the surprizing class
of oscillatory collision and ejection orbits. Using the infinity manifold,
we further tackle capture and escape solutions in the zero-energy case.
By finding the connection orbits between equilibria and/or cycles at impact
and at infinity, we describe a large class of capture-collision and
Refreshments will be served in Math Annex Room 1115, 3:15 p.m.