Description

• Title:
  Periodic solutions of perturbed Hamiltonian systems in the plane by the use of the Poincaré-Birkhoff theorem
• Creator:
  Fonda, Alessandro;
  Sabatini, Marco;
  Zanolin, Fabio
• Description:
  We prove the existence of periodic solutions for a planar non-autonomous Hamiltonian system which is a small perturbation of an autonomous system, in the presence of a non-isochronous period annulus. To this aim we use the Poincaré-Birkhoff fixed point theorem, even if the boundaries of the annulus are neither assumed to be invariant for the Poincaré map, nor to be star-shaped. As a consequence, we show how to deal with the problem of bifurcation of subharmonic solutions near a given nondegenerate periodic solution. In this framework, we only need little regularity assumptions, and we do not need to introduce any Melnikov type functions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2012.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 40, No 1 (September 2012); 29 - 52;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.021/8370
• Subject:
  Periodic solutions;
  Poincaré-Birkhoff;
  nonlinear dynamics;
  34C25;
  47H15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.021
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other