On computer-assisted proving the existence of periodic and bounded orbits

Roman Srzednicki

Published: 2015-09-30

Vol. 29 (2015)

On computer-assisted proving the existence of periodic and bounded orbits

Roman Srzednicki

Abstract

We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provide also some comments on computer-assisted proving in dynamics.

Keywords:

Poincaré map , Conley index , interval arithmetic , rigorous numerical algorithm

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Srzednicki, R. (2015). On computer-assisted proving the existence of periodic and bounded orbits. Annales Mathematicae Silesianae, 29, 7–17. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13973

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Vol. 29 (2015)
Published: 2015-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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