##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Seonhee Lim

#### Seoul National University

## Complex continued fractions and central limit theorem for rational trajectories

##### Abstract:

In this talk, we will first introduce the complex continued fraction maps associated with some imaginary quadratic fields ($d=1, 2, 3, 7, 11$) and their dynamical properties. Baladi-Vallee analyzed (real) Euclidean algorithms and proved the central limit theorem for rational trajectories and a wide class of cost functions measuring algorithmic complexity. They used spectral properties of an appropriate bivariate transfer operator and a generating function for certain Dirichlet series whose coefficients are essentially the moment generating function of the cost on the set of rationals. We extend the work of Baladi-Vallee for complex continued fraction maps mentioned above. (This is joint work with Dohyeong Kim and Jungwon Lee.)

Host: Brandon Seward

### April 21, 2022

### 10:00 AM

AP&M 6402

Zoom ID 967 4109 3409

Email an organizer for the password

Research Areas

Ergodic Theory and Dynamical Systems****************************