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

We consider a circular string in $\widehat{\gamma }$ deformed $AdS_5 \times T^{1,1}$whichislocalizedinthecenterof$AdS_5$ 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 $\widehat{\gamma }$. 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.