Total Variation of a Curve Under Chaos on the Real Line and on a Finite Graph

We show that if f : R → R is a continuous transitive map and γ : [ 0 , 1 ] → R is a nonconstant curve having finite total variation, then the total variation of f n ∘ γ tends to infinity exponentially as n → ∞ . A similar result is also proved for a Devaney chaotic map on a graph G .

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Veröffentlicht in:	Qualitative theory of dynamical systems 2024-02, Vol.23 (1), Article 16
Hauptverfasser:	Banerjee, Kuntal, Bhattacharyya, Anubrato, Mondal, Subhamoy
Format:	Artikel
Sprache:	eng
Schlagworte:	Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We show that if f : R → R is a continuous transitive map and γ : [ 0 , 1 ] → R is a nonconstant curve having finite total variation, then the total variation of f n ∘ γ tends to infinity exponentially as n → ∞ . A similar result is also proved for a Devaney chaotic map on a graph G .
ISSN:	1575-5460 1662-3592
DOI:	10.1007/s12346-023-00871-3