On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus

Erwan Lanneau[1]; Jean-Luc Thiffeault[2]

  • [1] Université du Sud Toulon-Var and Fédération de Recherches des Unités de Mathématiques de Marseille Centre de Physique Théorique (CPT) UMR CNRS 6207,Luminy, Case 907 13288 Marseille Cedex 9 (France)
  • [2] University of Wisconsin Department of Mathematics Van Vleck Hall, 480 Lincoln Drive Madison, WI 53706 (USA)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 1, page 105-144
  • ISSN: 0373-0956

Abstract

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We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus g = 2 to 5 , the minimum dilatation is the smallest Salem number for polynomials of degree 2 g .

How to cite

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Lanneau, Erwan, and Thiffeault, Jean-Luc. "On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus." Annales de l’institut Fourier 61.1 (2011): 105-144. <http://eudml.org/doc/219738>.

@article{Lanneau2011,
abstract = {We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus $g=2$ to $5$, the minimum dilatation is the smallest Salem number for polynomials of degree $2g$.},
affiliation = {Université du Sud Toulon-Var and Fédération de Recherches des Unités de Mathématiques de Marseille Centre de Physique Théorique (CPT) UMR CNRS 6207,Luminy, Case 907 13288 Marseille Cedex 9 (France); University of Wisconsin Department of Mathematics Van Vleck Hall, 480 Lincoln Drive Madison, WI 53706 (USA)},
author = {Lanneau, Erwan, Thiffeault, Jean-Luc},
journal = {Annales de l’institut Fourier},
keywords = {Pseudo-Anosov homeomorphism; small dilatation; flat surface; pseudo-Anosov homeomorphism},
language = {eng},
number = {1},
pages = {105-144},
publisher = {Association des Annales de l’institut Fourier},
title = {On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus},
url = {http://eudml.org/doc/219738},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Lanneau, Erwan
AU - Thiffeault, Jean-Luc
TI - On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 1
SP - 105
EP - 144
AB - We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus $g=2$ to $5$, the minimum dilatation is the smallest Salem number for polynomials of degree $2g$.
LA - eng
KW - Pseudo-Anosov homeomorphism; small dilatation; flat surface; pseudo-Anosov homeomorphism
UR - http://eudml.org/doc/219738
ER -

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