This paper asks whether the local stretching and contraction of chaotic dynamics can be inferred from a statistical transition model. It estimates the Jacobian of a discrete-time system from a matrix approximating the Perron-Frobenius transfer operator. The approach links transitions between state-space regions to local instability and dissipation without requiring explicit governing equations. Numerical experiments on one- and two-dimensional chaotic maps illustrate the reconstruction and its dependence on the available representation. Readers get a method for extracting local dynamical information from transfer operators and a clear starting point for assessing its use in sensitivity analysis.