Chaos in classical string dynamics in $\hat{\gamma }$ deformed $Ad{S}_5\times T^{1,1}$

Abstract

We consider a circular string in $\hat{\gamma }$ deformed $Ad{S}_5\times T^{1,1}$ which is localized in the center of $Ad{S}_5$ and winds around the two circles of deformed $T^{1,1}$. We observe chaos in the phase space of the circular string implying non-integrability of string dynamics. The chaotic behaviour in phase space is controlled by energy as well as the deforming parameter $\hat{\gamma }$. We further show that the point like object exhibits non-chaotic behaviour. Finally we calculate the Lyapunov exponent for both extended and point like object in support of our first result.

15 pages

References in corpus (4)

• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• On (non)integrability of classical strings in p-brane backgrounds
• Non-integrability in non-relativistic theories
• Chaos in Lifshitz Spacetimes

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