Closed orbits in quotient systems

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of East Anglia

Year dc:date.issued

2015

Author dc:creator

• Zegowitz, Stefanie

Language dc:language

en