SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 1

A recurrent set for one-dimensional dynamical systems

Seyyed Alireza AHMADİ
Pages
1–7
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This set is not necessarily invariant under continuous conjugacies, but it is invariant under absolutely continuous ones.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this note we introduce a new kind of recurrent set for a dynamical system on the interval [0,1].
📊
Key Findings & Data:In this note we introduce a new kind of recurrent set for a dynamical system on the interval [0,1].
💡
Conclusion & Impact:This set is not necessarily invariant under continuous conjugacies, but it is invariant under absolutely continuous ones.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Recurrent set · Chain recurrent set · Absolutely continuous map

Abstract

In this note we introduce a new kind of recurrent set for a dynamical system on the interval [0,1]. This set is not necessarily invariant under continuous conjugacies, but it is invariant under absolutely continuous ones.

🔖

Cite This Article

AHMADİ, S. A. (2022). A recurrent set for one-dimensional dynamical systems. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 1, 1–7. https://ajindex.com/articles/529882

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (2)

  1. S. A. Ahmadi. On the topology of the chain recurrent set of a dynamical system. Applied general topology, 15(2):167–174, 2014. J. M. Alongi and G. S. Nelson. Recurrence and topology, volume 85. American Mathematical Soc., 2007. N. Aoki and K. Hiraide. Topological theory of dynamical systems: recent advances, volume 52. Elsevier, 1994.
  2. P. Krupski, K. Omiljanowski, and K. Ungeheuer. Chain recurrent sets of generic mappings on compact spaces. Topology and its Applications, 202:251 – 268, 2016. S. Li. Dynamical properties of the shift maps on the inverse limit spaces. Ergodic Theory and Dynamical Systems, 12(01):95–108, 1992. N. Shekutkovski and M. Shoptrajanov. Intrinsic shape of the chain recurrent set. Topology and its Applications, 202:117 – 126, 2016. T. Shimomura. Special homeomorphisms and approximation for cantor systems. Topology and its Applications, 161:178 – 195, 2014. S. Spataru. An absolutely continuous function whose inverse functionis not absolutely continuous. Note di Matematica, 23(1):47–49, 2004. X. Wen and L. Wen. Codimension one structurally stable chain classes. Transactions of the American Mathematical Society, 368(6):3849–3870, 2016.