Description

• Title:
  Geometric proof of strong stable/unstable manifolds with application to the restricted three body problem
• Creator:
  Capiński, Maciej J.;
  Wasieczko-Zając, Anna
• Description:
  We present a method for establishing strong stable/unstable manifolds of fixed points for maps and ODEs. The method is based on cone conditions, suitably formulated to allow for application in computer assisted proofs. In the case of ODEs, assumptions follow from estimates on the vector field, and it is not necessary to integrate the system. We apply our method to the restricted three body problem and show that for a given choice of the mass parameter, there exists a homoclinic orbit along matching strong stable/unstable manifolds of one of the libration points.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 1 (September 2015); 363 - 399;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.051/7215
• Subject:
  Invariant manifolds;
  center manifolds;
  fixed points;
  34C45;
  34D35;
  37D10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.051
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other