Closed orbits in quotient systems
type: CreativeWork
description: 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.
abstract: 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.
author: Zegowitz, Stefanie
language: en
date published: 2015-01
date modified: 2026-07-24T02:12:10Z
provider: University of East Anglia
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of East Anglia