Closed orbits in quotient systems

Zegowitz, Stefanie (2015) Closed orbits in quotient systems. Doctoral thesis, University of East Anglia.

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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.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Brian Watkins
Date Deposited: 16 Sep 2015 11:28
Last Modified: 16 Sep 2015 11:28
URI: https://ueaeprints.uea.ac.uk/id/eprint/54400
DOI:

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