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Volume entropy of hyperbolic graph surfaces

Published online by Cambridge University Press:  09 February 2005

S. BUYALO
S. BUYALO
Affiliation:
Steklov Institute of Mathematics, Fontanka 27, 191011, St. Petersburg, Russia (e-mail: sbuyalo@pdmi.ras.ru)
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Abstract

A graph surface P is a two-dimensional polyhedron having the simplest kind of non-trivial singularities which result from gluing surfaces with compact boundaries along boundary components. We study the behavior of the volume entropy h(g) of hyperbolic metrics g on a closed graph surface P depending on the lengths of singular geodesics $Q\subset P$. We show that always h(g) > 1 and $h(g)\to\infty$ as $L_g(Q)\to\infty$ for at least one singular geodesic Q.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 2 , April 2005 , pp. 403 - 417
Copyright
2005 Cambridge University Press

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