North-South type dynamics of relative atoroidal automorphisms of free groups on a relative space of currents

Guerch, Yassine

doi:10.1090/ecgd/386

North-South type dynamics of relative atoroidal automorphisms of free groups on a relative space of currents
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by Yassine Guerch;

Conform. Geom. Dyn. 27 (2023), 161-263

DOI: https://doi.org/10.1090/ecgd/386

Published electronically: July 5, 2023

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Abstract:

This paper, which is the second of a series of three papers, studies dynamical properties of elements of $\operatorname {Out}(F_{\mathtt n})$, the outer automorphism group of a nonabelian free group $F_{\mathtt n}$. We prove that, for every exponentially growing outer automorphism of $F_{\mathtt n}$, there exists a preferred compact topological space, the space of currents relative to a malnormal subgroup system, on which $\phi$ acts by homeomorphism with a North-South dynamics behavior.

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