Selberg zeta functions, cuspidal accelerations, and existence of strict transfer operator approaches / Anke Pohl, Paul Wabnitz.

Format:

Book

Author/Creator:

Pohl, Anke, author.

Wabnitz, Paul, author.

Series:

Memoirs of the American Mathematical Society ; volume 318, number 1616.

Memoirs of the American Mathematical Society ; volume 318, number 1616

Language:

English

Subjects (All):

Dynamics.

Physical Description:

v, 156 pages : illustrations ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, 2026.

Summary:

For geometrically finite non-compact developable hyperbolic orbisurfaces (including those of infinite volume), we provide transfer operator families whose Fredholm determinants are identical to the Selberg zeta function. Our proof yields an algorithmic and uniform construction. This construction is initiated with an externally provided cross section for the geodesic flow on the considered orbisurface that yields a highly faithful, but non-uniformly expanding discrete dynamical system modelling the geodesic flow. Through a number of algorithmic steps of reduction, extension, translation, induction and acceleration, we turn this cross section into one that yields a still highly faithful, but now uniformly expanding discrete dynamical system. The arising transfer operator family is nuclear of order zero on suitable Banach spaces. In addition, finite-dimensional twists with non-expanding cusp monodromy can be included.

Notes:

Includes bibliographical references (pages 153-156).

ISBN:

1470478676

9781470478674

OCLC:

1579824480