Super-potentials, densities of currents and number of periodic points for holomorphic maps

Abstract

We prove that if a positive closed current is bounded by another one with bounded, continuous or Hoelder continuous super-potentials, then it inherits the same property. There are two different methods to define wedge-products of positive closed currents of arbitrary bi-degree on compact Kaehler manifolds using super-potentials and densities. When the first method applies, we show that the second method also applies and gives the same result. As an application, we obtain a sharp upper bound for the number of isolated periodic points of holomorphic maps on compact Kaehler manifolds whose actions on cohomology are simple. A similar result still holds for a large class of holomorphic correspondences.

28 pages; dedicated to Professor Le Tuan Hoa on the occasion of his sixtieth birthday

Cited by in corpus (3)

• Ergodic theorems for laminations and foliations: recent results and perspectives
• Densities of currents and complex dynamics
• An equidistribution theorem for biraitonal maps of ${\mathbb{P}}^k$