Numerical approximation of conditionally invariant measures via Maximum Entropy

It is well known that open dynamical systems can admit an un-countable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based selection scheme (essentially maximum entropy) for gaining numerical access to some of these mea-sures. The work is similar to the Maximum Entropy (MAXENT) approach for calculating absolutely continuous invariant measures of nonsingular dynamical systems, but contains some interesting new twists, including: (i) the natural escape rate is not known in advance, which can destroy convex structure in the problem; (ii) exploitation of convex duality to solve each approximation step induces important (but dynamically relevant and not at first apparent) localisation of support; (iii) significant potential for application to the approxima-tion of other dynamically interesting objects (for example, invariant manifolds)