Geodesic
Constructing pseudo-Anosovs from expanding interval maps
Ethan Farber1 orcid
1Boston College, Chestnut Hill, USA
Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 265-325

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DOI

We investigate a phenomenon observed by Thurston wherein one constructs a pseudo-Anosov homeomorphism on the limit set of a certain lift of a piecewise linear expanding interval map. We reconcile this construction with a special subclass of generalized pseudo-Anosovs, first defined by de Carvalho. From there we classify the circumstances under which this construction produces a pseudo-Anosov. As an application, we produce for each g≥1, a pseudo-Anosov φg​ on the closed surface of genus g that preserves an algebraically primitive translation structure and whose dilatation is a Salem number.
DOI : 10.4171/ggd/745
Classification : 37-XX, 57-XX
Mots-clés : Pseudo-Anosov, interval map, train track, Salem, entropy, stretch factor

Ethan Farber  1

1 Boston College, Chestnut Hill, USA 
Ethan Farber. Constructing pseudo-Anosovs from expanding interval maps. Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 265-325. doi: 10.4171/ggd/745
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     author = {Ethan Farber},
     title = {Constructing {pseudo-Anosovs} from expanding interval maps},
     journal = {Groups, geometry, and dynamics},
     pages = {265--325},
     year = {2024},
     volume = {18},
     number = {1},
     doi = {10.4171/ggd/745},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/745/}
}
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