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Title: Closed orbits in quotient systems
Author: Zegowitz, Stefanie
ISNI:       0000 0004 5352 5652
Awarding Body: University of East Anglia
Current Institution: University of East Anglia
Date of Award: 2015
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If we have topological conjugacy between two continuous maps, T : X → X and T 0 : X0 → X0 , then counts of closed orbits and periodic points are preserved. However, if we only have topological semi-conjugacy between T and T 0 , then anything is possible, and there is, in general, no relationship between closed orbits (or periodic points) of T and T 0 . However, if we let a finite group G act on X, where the action of G commutes with T and where we let X0 = G\X be the quotient of the action, then it is indeed possible to say a bit more about the relationship between the count of closed orbits of (X, T) and its quotient system (X0 , T0 ). In this thesis, we will describe the behaviour of closed orbits in quotient systems, and we will show that there exists a wide but restricted range of what growth rates can be achieved for these orbits. Moreover, we will examine the analytic properties of the dynamical zeta function in quotient systems.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available