Description

• Title:
  Milnor attractors and period incrementing on pattern iterations of flat top tent maps
• Creator:
  Silva, Luís;
  Silva, Teresa M.
• Description:
  In this paper, we consider the family of non-autonomous dynamical systems obtained by iterating tent maps with a flat top of constant value $u$ introduced at instants $i$ such that $s_i=0$, where $s$ is a binary sequence that we call the iteration pattern. We introduce symbolic dynamics and study the kneading invariants for these dynamical systems. More precisely, we define the kneading invariants $K(u,s)$ as symbolic sequences and study sufficient conditions for a symbolic sequence to be a kneading invariant $K(u,s)$ for some $u$, for each iteration pattern $s$. Finally, we describe the parameters $u$ for which there are Milnor attractors for iteration patterns $s$ such that $s_{np}=0$ for all $n$, as limits of parameter sequences corresponding to local attractors, organized according to a period-incrementing structure.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2025 Luís Silva, Teresa M. Silva
• Date:
  2025.02.13
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 65, No 1 (March 2025); 79 - 97;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/58806/41535 ;https://apcz.umk.pl/TMNA/article/view/58806/41536
• Subject:
  Non-autonomous dynamical systems;
  interval maps;
  attractors;
  symbolic dynamics;
  bifurcation diagrams;
  37E05, 37B55, 37G35, 37B10}%;
  Secondary: 46E25, 20C20
• Identifier: https://apcz.umk.pl/TMNA/article/view/58806
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other