Reduced dynamical systems

Luka Boc Thaler, Uroš Kuzman

Published 2019-02-12Version 1

We consider the dynamics of complex rational maps on the Riemann sphere. We prove that, after reducing their orbits to a fixed number of positive values representing the Fubini-Study distances between finitely many initial elements of the orbit and the origin, ergodic properties of the rational map are preserved.