HCRP project 2008
Caustic in surfaces which are paraboloid graphs
Caustics in various paraboloids
Office: SciCtr 434

Geodesic flow on elliptic paraboloid z=x2+2y2 starting at (0,0).
Geodesic flow on elliptic paraboloid z=x2+2y2 starting at point away from (0,0).
Geodesic flow on surface z=x4+y4 starting at (0,0).
Geodesic flow on surface z=x4+y4 starting away at (0,0).
Geodesic flow on surface z=x2+y2 starting away at (0,0).
Geodesic flow on surface z=x6+y6 starting at (0,0).
Geodesic flow on surface z=x6+y6 starting away from (0,0).
Geodesic flow on surface z=x2+y2 - a (x4+y4) starting at (0,0).
Questions and comments to knill@math.harvard.edu
Oliver Knill | Department of Mathematics | Harvard University