Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space

TL;DR

This paper explores the relationships between Patterson-Sullivan currents, generic stretching factors, and the asymmetric Lipschitz metric in Outer space, providing a quantitative framework connecting these concepts in geometric group theory.

Contribution

It introduces a novel quantitative relationship linking Patterson-Sullivan currents, generic stretching factors, and the asymmetric Lipschitz metric in Outer space.

Findings

Established a quantitative relationship between Patterson-Sullivan currents and the Lipschitz metric.

Connected generic stretching factors with Guirardel's intersection number.

Provided new insights into the geometry of Outer space.

Abstract

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number.