In this paper, we introduce an alternative method to calculate the topological entropy of each member of an infinite family of pseudo—Anosov braids on the finitely punctured disk making use of 𝛑𝟏- train tracks The method is based on Thurston’s theory of surface homeomorphisms and presents positive matrices alternative to Dynnikov matrices which compute the topological entropy of a given pseudo-Anosov braid.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we introduce an alternative method to calculate the topological entropy of each member of an infinite family of pseudo—Anosov braids on the finitely punctured disk making use of 𝛑𝟏- train tracks The method is based on Thurston’s theory of surface homeomorphisms and presents positive matrices alternative to Dynnikov matrices which compute the topological entropy of a given pseudo-Anosov braid.
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Key Findings & Data:In this paper, we introduce an alternative method to calculate the topological entropy of each member of an infinite family of pseudo—Anosov braids on the finitely punctured disk making use of 𝛑𝟏- train tracks The method is based on Thurston’s theory of surface homeomorphisms and presents positive matrices alternative to Dynnikov matrices which compute the topological entropy of a given pseudo-Anosov braid.
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Conclusion & Impact:In this paper, we introduce an alternative method to calculate the topological entropy of each member of an infinite family of pseudo—Anosov braids on the finitely punctured disk making use of 𝛑𝟏- train tracks The method is based on Thurston’s theory of surface homeomorphisms and presents positive matrices alternative to Dynnikov matrices which compute the topological entropy of a given pseudo-Anosov braid.
In this paper, we introduce an alternative method to calculate the topological entropy of each member of an infinite family of pseudo—Anosov braids on the finitely punctured disk making use of 𝛑𝟏- train tracks The method is based on Thurston’s theory of surface homeomorphisms and presents positive matrices alternative to Dynnikov matrices which compute the topological entropy of a given pseudo-Anosov braid.
Özet
Bu makalede, sonlu noktası çıkarılmış disk yüzeyinde tanımlı pseudo-Anosov tipinden örgülerin sonsuz bir ailesinin her bir üyesinin topolojik entropisi 𝛑𝟏- train track grafikleri yardımıyla hesaplanmıştır. Kullanılan yöntem Thurston’ın yüzey homeomorfizmaları kuramına dayanmakta ve ilgili pseudo-Anosov örgünün topolojik entropisini veren Dynnikov matrislere alternatif pozitif matrisler sunmaktadır.
Yurttas, S. O., Atay, A. (2021). Topological Entropy of Pseudo-Anosov Braids and Attracting Matrices. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 11 Sayı: 3, 2278–2289. https://doi.org/10.21597/jist.760097
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