Two-dimensional Blaschke Products: Degree growth and ergodic consequences

TL;DR

This paper investigates the dynamics of two-dimensional Blaschke products, focusing on how the degree of iterates grows and what this means for the map's ergodic behavior.

Contribution

It introduces new insights into the degree growth rates of 2D Blaschke products and explores their impact on ergodic properties, a novel analysis in higher dimensions.

Findings

Degree growth rates are characterized for 2D Blaschke products.

Ergodic properties are linked to the degree growth behavior.

New theoretical results connect dynamics and ergodic theory in multiple dimensions.

Abstract

We study the dynamics of Blaschke products in two dimensions, particularly the rates of growth of the degrees of iterates and the corresponding implications for the ergodic properties of the map.