##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Yan Mary He

#### University of Oklahoma

## A quantitative equidistribution of angles of multipliers of hyperbolic rational maps

##### Abstract:

In this talk, we will consider the angular component of multipliers of repelling cycles of a hyperbolic rational map in one complex variable. Oh-Winter have shown that these angles of multipliers uniformly distribute in the circle (-$\pi$, $\pi$]. Motivated by the sector problem in number theory, we show that for a fixed $K \gg 1$, almost all intervals of length $\frac{2 \pi}{K}$ in (-$\pi$, $\pi$] contains a multiplier angle with the property that the norm of the multiplier is bounded above by a polynomial in K. This is joint work with Hongming Nie.

Host: Brandon Seward

### March 10, 2022

### 12:00 PM

AP&M 7218

Zoom ID: 967 4109 3409

Password: dynamics

Research Areas

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