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Transfer Operators for the Geodesic Flow on Hyperbolic Surfaces

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Selberg Zeta Functions and Transfer Operators

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2139))

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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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  1. Mathematics Institute, University of Warwick, Coventry, UK

    Markus Szymon Fraczek

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  1. Markus Szymon Fraczek
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Fraczek, M.S. (2017). Transfer Operators for the Geodesic Flow on Hyperbolic Surfaces. In: Selberg Zeta Functions and Transfer Operators. Lecture Notes in Mathematics, vol 2139. Springer, Cham. https://doi.org/10.1007/978-3-319-51296-9_7

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