Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - BIF-SCV (Bifurcations in Several Complex Variables)

Teaser

The field of holomorphic dynamics in several complex variables is a fast-growing area of mathematics, linking complex geometry, dynamical systems and many other topics. This project addresses the central question of studying stability and bifurcations of such dynamical systems...

Summary

The field of holomorphic dynamics in several complex variables is a fast-growing area of mathematics, linking complex geometry, dynamical systems and many other topics. This project addresses the central question of studying stability and bifurcations of such dynamical systems under perturbation. The main objective are the establishing of a general stability theory valid for complex dynamical systems in any dimension, and a detailed understanding of the many differences with respect to the one dimensional case.

Work performed

During this action we could provide first detailed examples of degenerations of complex dynamical systems in two complex variables. This solved questions by leading researchers in the domain. We continued our work on the bifurcation of polynomial skew products and started a detailed study of measures of large entropy for endomorphisms of Pk.

Final results

In the coming months we expect to complete the works in progress mentioned above, leading to a clearer picture of both the bifurcation phenomena in higher dimensions and the properties of measures of large entropy for endomorphisms of Pk.

Website & more info

More info: http://wwwf.imperial.ac.uk/.