A Maximum-Entropy Meshfree Method for Computation of Invariant Measures

Abstract

Let $S$ : $X$ → $X$ be a nonsingular transformation such that the corresponding Frobenius-Perron operator $P$_S : $L$¹ ($X$) → $L$¹ ($X$) has a stationary density $f$^∗. We propose a maximum-entropy method based on a meshfree approach to the numerical recovery of $f$^∗. Numerical experiments show that this approach is more accurate than the maximum-entropy method based on piecewise linear functions, provided that the moments involved are known. Moreover, it has a smaller computational cost than the method mentioned.