BibTeX
@INCOLLECTION{
         Guckenheimer1996BAD,
       author = "John Guckenheimer",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "Bifurcations, Automatic Differentiation and Computer Generated Proofs",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "229--237",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Guckenheimer1996BAD",
       crossref = "Berz1996CDT",
       abstract = "Dynamical systems theory relies upon coordinate transformations to study
         qualitative properties of vector fields. These coordinate transformations depend upon derivatives of
         the vector fields as well as the values of the vector fields. Thus, automatic differentiation
         provides an attractive technology for studying dynamical systems. This paper describes one novel
         area in which this appears to be the case: computer validation of the phase portraits for families
         of planar vector fields. Hilbert's sixteenth problem is used to motivate interest in these
         results. The discussion is informal and new results are only sketched since the new algorithms for
         verifying properties of bifurcations have not been implemented and tested on examples.",
       keywords = "Dynamical systems, bifurcation, computer validation, phase portraits,
         Hilbert's sixteenth problem.",
       year = "1996"
}