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Transfer Operators for the Geodesic Flow on Hyperbolic Surfaces

  • Markus Szymon Fraczek
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2139)

Abstract

In this chapter we will discuss a transfer operator for the geodesic flow on hyperbolic surfaces, which Fredholm determinant gives the Selberg zeta function. The transfer operators we are interested in are a so-called nuclear operators of order zero, these operators have a well defined trace and can be approximated by operators of finite rank. Transfer operators can be also regarded as composition operators, for which an explicit trace formula can be found.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Markus Szymon Fraczek
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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