Open Math Notes

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Mary Pugh | University of Toronto
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University


Armand Azonnahin
Instituto de Matemática e Estatística da Universidade de São Paulo
Reference #


Posted date
2019-10-18 17:59:20
Revised date
2019-10-18 17:59:20
Notes type
   Research Monographs
      Complex Analysis
   Dynamical Systems and Ergodic Theory
      Discrete Time Systems
      Continuous Time Systems

On Cohomological Stochastic Dynamics of Higher Dimensions

Here is one of the best and the more recent books on Complex Dynamics in Higer Dimension. Here, we develop a calculus on positive closed currents of arbitrary bidegree on compact K{\"a}hler manifolds after
recalling a notion of super-potential associated to such currents by using deformations in the space of currents. We define in particular the intersection of such currents and the pull-back operator. We apply the theory of super-potentials to construct Green currents ...

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (2.0M) 10/18/19