Lyapunov Exponents and Phase Transitions of Born-Infeld AdS Black Holes

In this paper, we characterize the phase transitons of Born-Infeld AdS black holes in terms of Lyapunov exponents. We calculate the Lyapunov exponents for both null and timelike geodesics. It is found that black hole phase transitions can be described by multiple-valued Lyapunov exponents. And its phase diagram can be characterized by Lyapunov exponents and Hawking temperature. Besides, the change of Lyapunov exponents can be considered as order parameter, and exists a critical exponent $1\mathrm{/}2$ near critical point.