Description

• Title:
  On computer-assisted proving the existence of periodic and bounded orbits
• Creator:
  Srzednicki, Roman
• Description:
  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.
• Object availability:
  free access
• Date:
  2015.09.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol. 29 (2015); 7-17;
  Annales Mathematicae Silesianae; Tom 29 (2015); 7-17;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/13973/10673
• Subject:
  Poincaré map;
  Conley index;
  interval arithmetic;
  rigorous numerical algorithm
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/13973
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other