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The set of uniquely ergodic interval exchange transformations is path-connected

Published online by Cambridge University Press:  20 June 2017

JON CHAIKA  and
SEBASTIAN HENSEL
JON CHAIKA
Affiliation:
University of Utah, Department of Mathematics, 209 155 S 1400 E RM 233, Salt Lake City, UT, 84112-0090, USA email chaika@math.utah.edu
SEBASTIAN HENSEL
Affiliation:
Rheinische Friedrich-Wilhelms Universität Bonn, Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany email hensel@math.uni-bonn.de
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Abstract

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Let $\unicode[STIX]{x1D70B}$ be a non-degenerate permutation on at least four symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\unicode[STIX]{x1D70B}$ is path-connected.

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 2 , February 2019 , pp. 311 - 356
Copyright
© Cambridge University Press, 2017 

References

Athreya, J. and Chaika, J.. The Hausdorff dimension of non-uniquely ergodic directions in H(2) is almost everywhere 1/2. Geom. Topol. 18(5) (2014), 2683–2745.Google Scholar
Delecroix, V.. Cardinality of Rauzy classes. Ann. Inst. Fourier (Grenoble) 63(5) (2013), 1651–1715.Google Scholar
Gabai, D.. Almost filling laminations and the connectivity of ending lamination space. Geom. Topol. 13(2) (2009), 1017–1041.Google Scholar
Gabai, D.. On the topology of ending lamination space. Geom. Topol. 18(5) (2014), 2683–2745.Google Scholar
Hensel, S. and Przytycki, P.. The ending lamination space of the five-punctured sphere is the Nöbeling curve. J. Lond. Math. Soc. (2) 84(1) (2011), 103–119.Google Scholar
Katok, A. B. and Stepin, A. M.. Approximations in ergodic theory. Uspekhi Mat. Nauk 22(5 (137)) (1967), 81–106.Google Scholar
Keane, M.. Interval exchange transformations. Math. Z. 141 (1975), 25–31.Google Scholar
Leininger, C. and Schleimer, S.. Connectivity of the space of ending laminations. Duke Math. J. 150(3) (2009), 533–575.Google Scholar
Leininger, C. and Schleimer, S.. Hyperbolic spaces in Teichmüller spaces. J. Eur. Math. Soc. (JEMS) 16(12) (2014), 2669–2692.Google Scholar
Masur, H.. Interval exchange transformations and measured foliations. Ann. of Math. (2) 115(1) (1982), 169–200.Google Scholar
Masur, H. and Smillie, J.. Hausdorff dimension of sets of nonergodic measured foliations. Ann. of Math. (2) 134(3) (1991), 455–543.Google Scholar
Viana, M.. Ergodic theory of interval exchange maps. Rev. Mat. Complut. 19(1) (2006), 7–100.Google Scholar
Veech, W.. Interval exchange transformations. J. Anal. Math. 33 (1978), 222–272.Google Scholar
Veech, W.. Gauss measures for transformations on the space of interval exchange maps. Ann. of Math. (2) 115(1) (1982), 201–242.Google Scholar
Yoccoz, J.-C.. Interval exchange maps and translation surfaces. Homogeneous Flows, Moduli Spaces and Arithmetic, 169 (Clay Mathematics Proceedings, 10) . American Mathematical Society, Providence, RI, 2010.Google Scholar
Zorich, A.. Flat surfaces. Frontiers in Number Theory, Physics and Geometry I. Springer, Berlin, 2006, pp. 439–585.Google Scholar