Currents and Equidistribution in Holomorphic Dynamics.

Dynamical Systems;Equidistributiom;Ergodic Theory;Green Current;Mathematics;Science;Mathematics

Parra Casta, Manuel RodrigoZieve, Michael E. ;

University of Michigan

关键词: Dynamical Systems;    Equidistributiom;    Ergodic Theory;    Green Current;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/89619/rparra_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Given a holomorphic self-map of complex projective space of degree larger than one, we prove that there exists a finite collection of totally invariant algebraic sets with the following property: given any positive closed (1,1)-current of mass 1 with no mass on any element of this family, the sequence of normalized pull-backs of the current converges to the Green current. Under suitable geometric conditions on the collection of totally invariant algebraic sets, we prove a sharper equidistribution result.