Dynamically improper hypersurfaces for endomorphisms of projective space

Abstract

We introduce a new generalization of the notion of preperiodic hypersurface and explore some of its basic ramifications. We also prove that among nonlinear endomorphisms of projective space, those with a periodic critical point are Zariski dense. This answers a question of Ingram.

arXiv commentv4: 15 pages, reorganized; accepted to PAMS