arXiv Analytics

Sign in

arXiv:2211.11664 [math.DS]AbstractReferencesReviewsResources

On the generalised transfer operators of the Farey map with complex temperature

Claudio Bonanno

Published 2022-11-21Version 1

We consider the problem of showing that 1 is an eigenvalue for a family of generalised transfer operators of the Farey map. This problem is related to the spectral theory of the modular surface via the Selberg Zeta function and the theory of dynamical zeta functions of maps. After briefly recalling these connections, we show that the problem can be formulated for operators on an appropriate Hilbert space and translated into a linear algebra problem for infinite matrices.

Comments: 12 pages
Categories: math.DS, math-ph, math.MP
Subjects: 37C30, 37E05, 47B02
Related articles: Most relevant | Search more
arXiv:1103.5235 [math.DS] (Published 2011-03-27, updated 2011-08-11)
Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant
arXiv:1404.3934 [math.DS] (Published 2014-04-15)
A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area
arXiv:0907.1471 [math.DS] (Published 2009-07-09, updated 2011-06-03)
A thermodynamic approach to two-variable Ruelle and Selberg zeta functions via the Farey map

Links

Toolbox