Let F be a holomorphic correspondence defined on the complex sphere that admits a canonical invariant measure with good ergodic properties under certain natural conditions. The work of Dinh and Sibony shows that the normalized sums of point masses carried by the pre-images of a generic point under successive iterates of F converge to the canonical measure. Extending the theory of iterative dynamics of maps, the support of this canonical measure is a good candidate for the analogue of the Julia set in the context. In this talk, we shall investigate a basic question whether the analogues of the Julia set and the Fatou set dichotomise the complex plane.
Date and Time : 09-03-2017 14:00
Venue : Seminar Hall, 219 @ CET
Speaker : Shrihari Sridharan, IISER-TVM