Topological Entropy of Pseudo-Anosov Braids and Attracting Matrices

Öz

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.

Anahtar Kelimeler

• Topological entropy
• π1- train tracks
• pseudo-Anosov braids

Pseudo-Anosov Örgülerin Topolojik Entropisi ve Çekici Matrisler

Öz

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.

Anahtar Kelimeler

• Topolojik entropi
• π1- train track grafikleri
• pseudo-Anosov örgüler

Kaynakça

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