Maps over finite fields: integrability and reversibility

Prof. Franco Vivaldi

Queen Mary, University of London

In the theory of dynamical systems, integrability (existence of invariants of the motion) and reversibility (existence of conjugacy with inverse map) are important structural properties. We let two-dimensional algebraic mappings act on finite coordinate fields, and present experimental evidence for the existence of limit distributions of the length of the orbits for the integrable and reversible case. Such distributions feature considerable rigidity (independence from the mapping).