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

Roman Srzednicki

Annales Mathematicae Silesianae (2015)

  • Volume: 29, Issue: 1, page 7-17
  • ISSN: 0860-2107

Abstract

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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.

How to cite

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Roman Srzednicki. "On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits." Annales Mathematicae Silesianae 29.1 (2015): 7-17. <http://eudml.org/doc/276852>.

@article{RomanSrzednicki2015,
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.},
author = {Roman Srzednicki},
journal = {Annales Mathematicae Silesianae},
keywords = {Poincarémap; Conley index; interval arithmetic; rigorous numerical algorithm},
language = {eng},
number = {1},
pages = {7-17},
title = {On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits},
url = {http://eudml.org/doc/276852},
volume = {29},
year = {2015},
}

TY - JOUR
AU - Roman Srzednicki
TI - On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits
JO - Annales Mathematicae Silesianae
PY - 2015
VL - 29
IS - 1
SP - 7
EP - 17
AB - 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.
LA - eng
KW - Poincarémap; Conley index; interval arithmetic; rigorous numerical algorithm
UR - http://eudml.org/doc/276852
ER -

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