On the spectrum of Farey and Gauss maps

Details On the spectrum of Farey and Gauss maps On the spectrum of Farey and Gauss maps

2003-08-04

arxiv.org/abs/math/0308017v1

Nonlinearity 15 (2002), pp. 1521-1539

Mathematics

Dynamical Systems

23 pages

Scientific paper

10.1088/0951-7715/15/5/310

In this paper we introduce Hilbert spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced version, the Gauss map, respectively. By means of a suitable operator-valued power series we are able to study simultaneously the spectrum of both these operators along with the analytic properties of the associated dynamical zeta functions.

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