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arXiv:math/0308017 [math.DS]AbstractReferencesReviewsResources

On the spectrum of Farey and Gauss maps

Stefano Isola

Published 2003-08-04Version 1

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.

Comments: 23 pages
Journal: Nonlinearity 15 (2002), pp. 1521-1539
Categories: math.DS, math.SP
Subjects: 58F20, 58F25, 11F72, 11M26
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