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Journals / Fırat Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2004 / Cilt: 16 - Sayı: 1

Expansive $Z^d$ sonlu tipli altkaydırma için entropi

The entropy for expansive $Z^d$ subshifts of finite type

Hasan AKIN
Seyit TEMİR
Pages
131–137
Publication Date
2022-10-17
DOI
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AI Summary & Key Takeaways

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

We show that $h_{top}(sigma)= h_{span}(sigma) = h_{sep}(sigma)$ if a is expansive $Z^d$ shift action.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, firstly, $Z^d$ action is investigated without going into details.
📊
Key Findings & Data:Then, the metric entropy and the topological entropy of this dynamic system obtained according to $Z^2$ action by using Bowen's definition are defined.
💡
Conclusion & Impact:We show that $h_{top}(sigma)= h_{span}(sigma) = h_{sep}(sigma)$ if a is expansive $Z^d$ shift action.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, firstly, $Z^d$ action is investigated without going into details. Then, the metric entropy and the topological entropy of this dynamic system obtained according to $Z^2$ action by using Bowen's definition are defined. Lastly, the topological and the metric entropy of 2-dimensional subshift of finite type obtained according to $Z^2$ actions are analysed. We show that $h_{top}(sigma)= h_{span}(sigma) = h_{sep}(sigma)$ if a is expansive $Z^d$ shift action.

Özet

Bu çalışmada ilk olarak detaya girilmeksizin $Z^d$ aksiyonu incelenmektedir. Daha sonra $Z^2$ aksiyonuna göre elde edilmiş dinamik sistemin metrik ve topolojik entropisi Bowen'in tanımı kullanılarak tanımlanmaktadır. Son olarakta, $Z^2$ aksiyonuna göre elde edilmiş 2 boyutlu sonlu tipli altkaydırmanın topolojik ve metrik entropisi analiz edilmektedir. Eğer $sigma$, bir expansive $Z^d$ kaydırma aksiyonu ise o zaman $h_{top}(sigma)= h_{span}(sigma) = h_{sep}(sigma)$ eşitliğinin geçerli olduğu gösterilmektedir.

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Cite This Article

AKIN, H., TEMİR, S. (2022). Expansive $Z^d$ sonlu tipli altkaydırma için entropi. Fırat Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 16 - Sayı: 1, 131–137. https://ajindex.com/articles/513674

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References (8)

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