Publication: Bifurcations, Automatic Differentiation and Computer Generated Proofs
Introduction
Applications
Tools
Research Groups
Workshops
Publications
   List Publications
   Advanced Search
   Info
   Add Publications
My Account
About

Bifurcations, Automatic Differentiation and Computer Generated Proofs

- incollection -
 

Author(s)
John Guckenheimer

Published in
Computational Differentiation: Techniques, Applications, and Tools

Editor(s)
Martin Berz, Christian Bischof, George Corliss, Andreas Griewank

Year
1996

Publisher
SIAM

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.

Cross-References
Berz1996CDT

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"
}


back
  

Contact:
autodiff.org
Username:
Password:
(lost password)