FROM RUELLE TRANSFER OPERATOR TO THE SCHRODINGER OPERATOR

We show that Ruelle's transfer operator, defined for an appropriate class of strongly chaotic mappings, reduces to the Schrodinger operator (with imaginary time) in an appropriate scaling limit. We also derive the equations for the next-order corrections to the Schrodinger behavior if the scaling limit is not completely performed. In the simplest case, the first-order correction turns out to obey a Schrijdinger equation with a source term. This means, a possible chaotic dynamics underlying the Feynman-Kac formula on a very small time scale (e.g., the Planck scale) leads to a generalized quantum mechanics with an additional source term.