scholarly journals On Sarnak’s conjecture and Veech’s question for interval exchanges

2018 ◽  
Vol 134 (2) ◽  
pp. 545-573 ◽  
Author(s):  
Sébastien Ferenczi ◽  
Christian Mauduit
Keyword(s):  
Interval Exchanges

scholarly journals Bifix codes and interval exchanges

2015 ◽  
Vol 219 (7) ◽  
pp. 2781-2798 ◽  
Author(s):  
Valérie Berthé ◽  
Clelia De Felice ◽  
Francesco Dolce ◽  
Julien Leroy ◽  
Dominique Perrin ◽  
...  
Keyword(s):  
Interval Exchanges

Generalized interval exchanges and the 2–3 conjecture

2005 ◽  
Vol 3 (3) ◽  
pp. 412-429
Author(s):  
Shmuel Friedland ◽  
Benjamin Weiss
Keyword(s):  
Interval Exchanges

scholarly journals Rigidity and Substitutive Dendric Words

2018 ◽  
Vol 29 (05) ◽  
pp. 705-720 ◽  
Author(s):  
V. Berthé ◽  
F. Dolce ◽  
F. Durand ◽  
J. Leroy ◽  
D. Perrin
Keyword(s):  
Bipartite Graphs ◽  
Constant Length ◽  
Infinite Words ◽  
Algebraic Properties ◽  
Interval Exchanges ◽  
Left And Right ◽  
Sturmian Words

Dendric words are infinite words that are defined in terms of extension graphs. These are bipartite graphs that describe the left and right extensions of factors. Dendric words are such that all their extension graphs are trees. They are also called tree words. This class of words includes classical families of words such as Sturmian words, codings of interval exchanges, or else, Arnoux–Rauzy words. We investigate here the properties of substitutive dendric words and prove some rigidity properties, that is, algebraic properties on the set of substitutions that fix a dendric word. We also prove that aperiodic minimal dendric subshifts (generated by dendric words) cannot have rational topological eigenvalues, and thus, cannot be generated by constant length substitutions.

scholarly journals Interval exchanges that do not occur in free groups

2012 ◽  
Vol 6 (4) ◽  
pp. 755-763 ◽  
Author(s):  
Christopher Novak
Keyword(s):  
Free Groups ◽  
Interval Exchanges

Cutting and stacking, interval exchanges and geometric models

1985 ◽  
Vol 50 (1-2) ◽  
pp. 160-168 ◽  
Author(s):  
Pierre Arnoux ◽  
Donald S. Ornstein ◽  
Benjamin Weiss
Keyword(s):  
Geometric Models ◽  
Interval Exchanges ◽  
Cutting And Stacking

scholarly journals An alternative approach to the ergodic theory of measured foliations on surfaces

1981 ◽  
Vol 1 (4) ◽  
pp. 461-488 ◽  
Author(s):  
Mary Rees
Keyword(s):  
Projective Space ◽  
Lebesgue Measure ◽  
Ergodic Theory ◽  
Diffeomorphism Group ◽  
Alternative Approach ◽  
Interval Exchanges ◽  
Almost All ◽  
Uniquely Ergodic

AbstractWe consider measured foliations on surfaces, and interval exchanges. We give alternative proofs of the following theorems first proved by Masur and (independently) Veech. The action of the diffeomorphism group of the surface on the projective space of measured foliations (with respect to a natural ‘Lebesgue’ measure) is ergodic. Almost all measured foliations are uniquely ergodic. Almost all interval exchanges (again, with respect to a natural ‘Lebesgue’ measure) are uniquely ergodic.

scholarly journals Infinite interval exchange transformations from shifts

2016 ◽  
Vol 37 (6) ◽  
pp. 1935-1965 ◽  
Author(s):  
LUIS-MIGUEL LOPEZ ◽  
PHILIPPE NARBEL
Keyword(s):  
Topological Entropy ◽  
Interval Exchange ◽  
Infinite Interval ◽  
Linear Factor ◽  
Interval Exchange Transformations ◽  
Interval Exchanges ◽  
Finiteness Properties ◽  
Block Growth ◽  
Linear Block

We show that minimal shifts with zero topological entropy are topologically conjugate to interval exchange transformations, which are generally infinite. When these shifts have linear factor complexity (linear block growth), the conjugate interval exchanges are proved to satisfy strong finiteness properties.

Sign in / Sign up

Export Citation Format

Share Document