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

@article{Kapovich2014PattersonSullivanCG, title={Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space}, author={Ilya Kapovich and Martin Lustig}, journal={arXiv: Group Theory}, year={2014} }

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.

## 2 Citations

### Spectral theorems for random walks on mapping class groups and Out(FN)

- Mathematics
- 2021

We establish spectral theorems for random walks on mapping class groups of connected, closed, oriented, hyperbolic surfaces, and on Out(FN ). In both cases, we relate the asymptotics of the…

### Spectral Theorems for Random Walks on Mapping Class Groups and Out $(\boldsymbol{F}_{\boldsymbol{N}})$

- Mathematics
- 2015

We establish spectral theorems for random walks on mapping class groups of connected, closed, oriented, hyperbolic surfaces, and on $\text{Out}(F_N)$. In both cases, we relate the asymptotics of the…

## References

SHOWING 1-10 OF 66 REFERENCES

### A Weil–Petersson type metric on spaces of metric graphs

- Mathematics
- 2014

In this note, we discuss an analogue of the Weil–Petersson metric for spaces of metric graphs and some of its properties.

### An algorithm to detect full irreducibility by bounding the volume of periodic free factors

- Mathematics
- 2014

We provide an effective algorithm for determining whether an element φ of the outer automorphism group of a free group is fully irreducible. Our method produces a finite list that can be checked for…

### Current twisting and nonsingular matrices

- Mathematics
- 2009

We show that for k at least 3, given any matrix in GL(k,Z), there is a hyperbolic fully irreducible automorphism of the free group of rank k whose induced action on Z^k is the given matrix.

### Growth of intersection numbers for free group automorphisms

- Mathematics
- 2010

For a fully irreducible automorphism ϕ of the free group Fk we compute the asymptotics of the intersection number n ↦ i(T, T′ϕn) for the trees T and T′ in Outer space. We also obtain qualitative…

### A Bers-like proof of the existence of train tracks for free group automorphisms

- Mathematics
- 2010

Using Lipschitz distance on Outer space we give another proof of the train track theorem.

### Non-uniquely ergodic foliations of thin type

- MathematicsErgodic Theory and Dynamical Systems
- 1997

We construct a minimal foliation of thin type which is not uniquely ergodic. The notion of thin type relates to Rips' classification of foliations on 2-complexes.

### Strongly Contracting Geodesics in Outer Space

- Mathematics
- 2008

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that…

### The Patterson–Sullivan Embedding and Minimal Volume Entropy for Outer Space

- Mathematics
- 2007

Abstract.Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map from the Culler–Vogtmann outer space CV (Fk) into the space of…