Chaos in Lifshitz spacetimes

We investigate the chaotic behavior of a circular test string in the Lifshitz spacetimes by considering the critical exponent z as an external control parameter. We demonstrate that two primary tools to observe chaos in this system are the Poincaré section and the Lyapunov exponent. Finally, the numerical result shows that if z = 1, the string dynamics is regular while in a case slightly larger than z = 1, the dynamics can be irregular and chaotic, which implies that the space time anisotropy, which breaks Lorentz symmetry, may cause the system to be chaotic.