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).