American Institute of Mathematical Sciences

Advanced
February  2010, 27(1): 53-73. doi: 10.3934/dcds.2010.27.53

Disjointness of interval exchange transformations from systems of probabilistic origin

Jacek Brzykcy 1, and  Krzysztof Frączek 1,

1. 

Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

Received  May 2009 Revised  September 2009 Published  February 2010

We prove the disjointness of almost all interval exchange transformations from ELF systems (systems of probabilistic origin) for a countable subset of permutations including the symmetric permutations

$ 1\ 2\ \ldots \ m-1 \ m $
$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m\ m-1 \ldots \ 2\ 1 $ for m=3,5,7.

Some disjointness properties of special flows built over interval exchange transformations and under piecewise constant roof function are investigated as well.

Keywords: disjointness of dynamical systems., Interval exchange transformations.
Mathematics Subject Classification: 37A05, 37E0.
Citation: Jacek Brzykcy, Krzysztof Frączek. Disjointness of interval exchange transformations from systems of probabilistic origin. Discrete & Continuous Dynamical Systems, 2010, 27 (1) : 53-73. doi: 10.3934/dcds.2010.27.53
[1]

Jon Chaika, Alex Eskin. Möbius disjointness for interval exchange transformations on three intervals. Journal of Modern Dynamics, 2019, 14: 55-86. doi: 10.3934/jmd.2019003
[2]

Ivan Dynnikov, Alexandra Skripchenko. Minimality of interval exchange transformations with restrictions. Journal of Modern Dynamics, 2017, 11: 219-248. doi: 10.3934/jmd.2017010
[3]

Sébastien Ferenczi, Pascal Hubert. Rigidity of square-tiled interval exchange transformations. Journal of Modern Dynamics, 2019, 14: 153-177. doi: 10.3934/jmd.2019006
[4]

Luca Marchese. The Khinchin Theorem for interval-exchange transformations. Journal of Modern Dynamics, 2011, 5 (1) : 123-183. doi: 10.3934/jmd.2011.5.123
[5]

Jon Chaika. Hausdorff dimension for ergodic measures of interval exchange transformations. Journal of Modern Dynamics, 2008, 2 (3) : 457-464. doi: 10.3934/jmd.2008.2.457
[6]

Jon Chaika, David Damanik, Helge Krüger. Schrödinger operators defined by interval-exchange transformations. Journal of Modern Dynamics, 2009, 3 (2) : 253-270. doi: 10.3934/jmd.2009.3.253
[7]

Corinna Ulcigrai. Weak mixing for logarithmic flows over interval exchange transformations. Journal of Modern Dynamics, 2009, 3 (1) : 35-49. doi: 10.3934/jmd.2009.3.35
[8]

Giovanni Forni. On the Brin Prize work of Artur Avila in Teichmüller dynamics and interval-exchange transformations. Journal of Modern Dynamics, 2012, 6 (2) : 139-182. doi: 10.3934/jmd.2012.6.139
[9]

Giovanni Forni, Carlos Matheus. Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards. Journal of Modern Dynamics, 2014, 8 (3&4) : 271-436. doi: 10.3934/jmd.2014.8.271
[10]

Silvére Gangloff, Alonso Herrera, Cristobal Rojas, Mathieu Sablik. Computability of topological entropy: From general systems to transformations on Cantor sets and the interval. Discrete & Continuous Dynamical Systems, 2020, 40 (7) : 4259-4286. doi: 10.3934/dcds.2020180
[11]

Carlos Gutierrez, Simon Lloyd, Vladislav Medvedev, Benito Pires, Evgeny Zhuzhoma. Transitive circle exchange transformations with flips. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 251-263. doi: 10.3934/dcds.2010.26.251
[12]

Denis de Carvalho Braga, Luis Fernando Mello, Carmen Rocşoreanu, Mihaela Sterpu. Lyapunov coefficients for non-symmetrically coupled identical dynamical systems. Application to coupled advertising models. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 785-803. doi: 10.3934/dcdsb.2009.11.785
[13]

Christopher F. Novak. Discontinuity-growth of interval-exchange maps. Journal of Modern Dynamics, 2009, 3 (3) : 379-405. doi: 10.3934/jmd.2009.3.379
[14]

Marta Štefánková. Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval. Discrete & Continuous Dynamical Systems, 2016, 36 (6) : 3435-3443. doi: 10.3934/dcds.2016.36.3435
[15]

Piotr Oprocha. Double minimality, entropy and disjointness with all minimal systems. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 263-275. doi: 10.3934/dcds.2019011
[16]

Jon Chaika, Howard Masur. There exists an interval exchange with a non-ergodic generic measure. Journal of Modern Dynamics, 2015, 9: 289-304. doi: 10.3934/jmd.2015.9.289
[17]

Davit Karagulyan. Hausdorff dimension of a class of three-interval exchange maps. Discrete & Continuous Dynamical Systems, 2020, 40 (3) : 1257-1281. doi: 10.3934/dcds.2020077
[18]

P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of host-parasite systems. Global analysis. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 1-17. doi: 10.3934/dcdsb.2007.8.1
[19]

Wen Huang, Zhiren Wang, Guohua Zhang. Möbius disjointness for topological models of ergodic systems with discrete spectrum. Journal of Modern Dynamics, 2019, 14: 277-290. doi: 10.3934/jmd.2019010
[20]

Matteo Petrera, Yuri B. Suris. Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. Ⅱ. Systems with a linear Poisson tensor. Journal of Computational Dynamics, 2019, 6 (2) : 401-408. doi: 10.3934/jcd.2019020

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (65)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences