  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 $1/2$ near critical point.
