Dynamical Approximations of Postsingularly Finite Entire Maps

Explore the dynamics of entire maps of finite type in this lecture from the Simons Semester on Dynamics. Delve into the concept of postsingularly finite maps and their significance in understanding global dynamics. Learn about a groundbreaking study that demonstrates how postsingularly finite maps can be approximated by a sequence of postsingularly finite polynomials, preserving key dynamical properties. Discover the connections between these approximations, their combinatorics, and maps acting on Teichmuller spaces. Gain insights into how this research contributes to the broader understanding of complex dynamics and the behavior of maps with finitely many singular values.