Constructing pseudo-Anosov maps with given dilatations

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• 作者：Hyungryul Baik ; Ahmad Rafiqi ; Chenxi Wu
• 关键词：Pseudo ; Anosov ; Dilatation ; Perron ; 37B40 ; 37E30 ; 54H20
• 刊名：Geometriae Dedicata
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：180
• 期：1
• 页码：39-48
• 全文大小：949 KB
• 参考文献：1.de Carvalho, A., Hall, T.: Unimodal generalized pseudo-Anosov maps. Geom. Topol. 8, 1127–1188 (2004)CrossRef MathSciNet MATH
  2.Farb, B.: Some problems on mapping class groups and moduli space. Problems on mapping class groups and related topics. Proc. Sympos. Pure Math. 74, 11–55 (2006)CrossRef MathSciNet
  3.Fried, D.: Growth rate of surface homeomorphisms and flow equivalence. Ergod. Theory Dyn. Syst. 5(04), 539–563 (1985)CrossRef MATH
  4.Lind, D.A.: The Entropies of Topological Markov Shifts and a Related Class of Algebraic Integers. Mathematical Sciences Research Institute, Berkeley (1984)
  5.Thurston, W.: Entropy in dimension one. arXiv:​1402.​2008 (2014)
  
• 作者单位：Hyungryul Baik (1)
  Ahmad Rafiqi (2)
  Chenxi Wu (3)
  
  1. Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany
  2. Department of Mathematics, Cornell University, 111 Malott Hall, Ithaca, NY, 14853, USA
  3. Department of Mathematics, Cornell University, 105 Malott Hall, Ithaca, NY, 14853, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9168

文摘

In this paper, we give sufficient conditions for a Perron number, given as the leading eigenvalue of an aperiodic matrix, to be a pseudo-Anosov dilatation of a compact surface. We give an explicit construction of the surface and the map when the sufficient condition is met. Keywords Pseudo-Anosov Dilatation Perron