<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6 30–348 Kraków, Poland

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits"}

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...

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

Published Online: Sep 30, 2015

Page range: 7 - 17

Received: Mar 01, 2015

DOI: https://doi.org/10.1515/amsil-2015-0001

© Roman Srzednicki

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.