**8:45 AM / Thursday, February 15, 1996**
### Invited Presentation 6

Bifurcations, Automatic Differentiation and Computer Generated Proofs

Estimating the errors in calculations of trajectories of a dynamical system is exceedingly difficult. Nonetheless, it is possible to prove many properties of low dimensional dynamical systems with methods that rely upon transversality arguments and local coordinate transformations. This approach to computer generated proofs for dynamical systems uses computations of derivatives and interval arithmetic. These two tools can be combined in an approach to the rigorous computation of bifurcation diagrams in multiparameter vector fields.
**John Guckenheimer**

Cornell University

MEM, 12/28/95