Abstract Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, control. There is an intricate connection between dynamical systems driven by stochastic differential equations quant...

Abstract This paper deals with some analytic aspects of GG system introduced by I.M. Gelfand and M.I. Graev: we compute the dimension solution space over field meromorphic functions periodic respect to a lattice. We describe monodromy invariant subspace space. provide connection formula between pair bases consisting $\Gamma $-series solutions associated regular triangulations adjacent each othe...