Description

• Title:
  Invariance of bifurcation equations for high degeneracy bifurcations of non-autonomous periodic maps
• Creator:
  Oliveira, Henrique M.
• Description:
  Bifurcations of the class $A_{\mu}$, in Arnold's classification, in non-autonomous $p$-periodic difference equations generated by parameter depending families with $p$ maps, are studied. It is proved that the conditions of degeneracy, non-degeneracy and unfolding are invariant relatively to cyclic order of compositions for any natural number $\mu$. The main tool for the proofs is the local topological conjugacy. Invariance results are essential for proper definition of bifurcations of the class $A_{\mu}$ and associated lower codimension bifurcations, using all possible cyclic compositions of fiber families of maps of the $p$-periodic difference equation. Finally, we present two examples of the class $A_{3}$ or swallowtail bifurcation occurring in period two difference equations for which bifurcation conditions are invariant.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 47, No 2 (June 2016); 715 - 737;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.031/8184 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.031/8185
• Subject:
  Topological conjugacy;
  $A_\mu$ degenerate bifurcation;
  non-autonomous map;
  p-periodic map;
  alternating system;
  Primary;
  37G15;
  Secondary;
  39A28
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.031
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other