Abstract: Periodic points of dominant rational self-maps on algebraic varieties have bounded height in several dynamically interesting cases, such as polarized endomorphisms or Henon maps. It is conjectured that the set of isolated periodic points of an automorphism of an affine space is a set of bounded height. We give a counterexample to this conjecture. As a positive result, we prove that any cohomologically hyperbolic dominant rational self-map on a projective variety admits a non-empty Zariski open subset on which the set of periodic points is height bounded. This talk is based on a joint work with Kaoru Sano.