Complex dynamics and invariant forms mod p

Abstract

Complex dynamical systems on the Riemann sphere do not possess ``invariant forms''. However there exist non-trivial examples of dynamical systems, defined over number fields, satisfying the property that their reduction modulo $\wp$ possesses ``invariant forms'' for all but finitely many places $\wp$. The paper completely characterizes those dynamical systems possessing the latter property.

revised version to appear in IMRN