Rigorous statistical procedures for data from dynamical systems - Denker, Manfred; Keller, Gerhard (Journal of Statistical Physics, 1986)
Various questions about the invariant measures of a dynamical system can be answered by computations of regular functionals or by ranking methods based on a set of observations. This includes symmetry tests and the determination of dimension coefficients. The paper contains the theoretical results and several simulations explain the methods.
Keywords: Dynamical systems; invariant measure; Hausdorff dimension; symmetric densities; U statistics; rank statistics