Entropy of polynomial and rational maps


In this note we define an entropy of rational maps of a smooth projective variety X to itself in terms of the growth rate of the volumes of its subvarieties. We give a formula for this entropy in terms of the spectral radius of the iterates of the induced maps on the homology subgroups of $X$ generated by analytic cycles. In the case of holomorphic maps we show that this entropy is the standard entropy which is equal to the log of the spectral radius of the induced map on the homology.


Shmuel Friedland