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Title: Resonances for graph directed Markov systems, and geometry of infinitely generated dynamical systems
Author: Hille, Martial R.
ISNI:       0000 0004 2717 7172
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 2009
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In the first part of this thesis we transfer a result of Guillopé et al. concerning the number of zeros of the Selberg zeta function for convex cocompact Schottky groups to the setting of certain types of graph directed Markov systems (GDMS). For these systems the zeta function will be a type of Ruelle zeta function. We show that for a finitely generated primitive conformal GDMS S, which satisfies the strong separation condition (SSC) and the nestedness condition (NC), we have for each c>0 that the following holds, for each w \in\$C$ with Re(w)>-c, |\Im(w)|>1 and for all k \in\$N$ sufficiently large: log | zeta(w) | <
Supervisor: Stratmann, Bernd O. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Resonances ; Graph directed Markov systems ; Hausdorff dimension ; Zeta function ; Limit set ; Discrepancy type