scholarly journals Dilation surfaces and their Veech groups

2019 ◽  
Vol 14 (1) ◽  
pp. 121-151
Author(s):  
Eduard Duryev ◽  
◽  
Charles Fougeron ◽  
Selim Ghazouani ◽  
◽  
...  
Keyword(s):  
Veech Groups

scholarly journals Congruence Veech groups

2016 ◽  
Vol 214 (2) ◽  
pp. 885-930
Author(s):  
Myriam Finster
Keyword(s):  
Veech Groups

scholarly journals Veech groups without parabolic elements

2006 ◽  
Vol 133 (2) ◽  
pp. 335-346 ◽  
Author(s):  
Pascal Hubert ◽  
Erwan Lanneau
Keyword(s):  
Veech Groups

Infinitely generated Veech groups

2004 ◽  
Vol 123 (1) ◽  
pp. 49-69 ◽  
Author(s):  
Pascal Hubert ◽  
Thomas A. Schmidt
Keyword(s):  
Veech Groups

scholarly journals Cascades in the dynamics of affine interval exchange transformations

2019 ◽  
Vol 40 (8) ◽  
pp. 2073-2097
Author(s):  
ADRIEN BOULANGER ◽  
CHARLES FOUGERON ◽  
SELIM GHAZOUANI
Keyword(s):  
Cantor Set ◽  
Parameter Family ◽  
Interval Exchange ◽  
Link Type ◽  
Interval Exchange Transformations ◽  
Veech Group ◽  
Veech Groups ◽  
Rauzy Induction

We describe in this article the dynamics of a one-parameter family of affine interval exchange transformations. This amounts to studying the directional foliations of a particular dilatation surface introduced in Duryev et al [Affine surfaces and their Veech groups. Preprint, 2016, arXiv:1609.02130], the Disco surface. We show that this family displays various dynamical behaviours: it is generically dynamically trivial but for a Cantor set of parameters the leaves of the foliations accumulate to a (transversely) Cantor set. This study is achieved through analysis of the dynamics of the Veech group of this surface combined with a modified version of Rauzy induction in the context of affine interval exchange transformations.

scholarly journals Non-congruence of homology Veech groups in genus two

2018 ◽  
Vol 201 (1) ◽  
pp. 253-280
Author(s):  
Christian Weiß
Keyword(s):  
Veech Groups ◽  
Genus Two

scholarly journals Classification of Rauzy–Veech groups: proof of the Zorich conjecture

2018 ◽  
Vol 215 (3) ◽  
pp. 741-778 ◽  
Author(s):  
Rodolfo Gutiérrez-Romo
Keyword(s):  
Veech Groups
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