https://doi.org/10.1140/epjc/s10052-016-4148-z
Regular Article - Theoretical Physics
Dynamical behavior and Jacobi stability analysis of wound strings
1
The Institute for Fundamental Study, “The Tah Poe Academia Institute”, Naresuan University, Phitsanulok, 65000, Thailand
2
Thailand Center of Excellence in Physics, Ministry of Education, Bangkok, 10400, Thailand
3
Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084, Cluj-Napoca, Romania
4
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
* e-mail: t.harko@ucl.ac.uk
Received:
22
December
2015
Accepted:
17
May
2016
Published online:
4
June
2016
We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of 
, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an 
of constant radius 
. We then use Kosambi–Cartan–Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective 
-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.
© The Author(s), 2016
