|Date||Oct 25, 2022|
In this talk, I start with the ergodic theory of the simple continued fraction map for real numbers from a historical point of view. Then I explain how we follow it for the comlex case. There are a number of complex continued fraction maps that give continued fraction expansions of complex numbers.
The main issue is the construction of the natural extension of each map, which is defined
on the three-dimensional hyperbolic space.