2010, 26(1): 251-263. doi: 10.3934/dcds.2010.26.251

Transitive circle exchange transformations with flips

1. 

ICMC-USP, São Carlos, Caixa Postal 668, CEP 13560-970, São Carlos, SP

2. 

School of Mathematics and Statistics, University of New South Wales, Sydney

3. 

Institute of Applied Mathematics and Cybernetics, Nizhny Novgorod State University, Nizhny Novgorod, Russian Federation

4. 

Departamento de Física e Matemática, Universidade de São Paulo, Ribeirão Preto - SP, Brazil

5. 

Department of Mathematics and Physics, Nizhny Novgorod State Pedagogical University, Nizhny Novgorod, Russian Federation

Received  October 2008 Revised  June 2009 Published  October 2009

We study the existence of transitive exchange transformations with flips defined on the unit circle $S^1$. We provide a complete answer to the question of whether there exists a transitive exchange transformation of $S^1$ defined on $n$ subintervals and having $f$ flips.
Citation: Carlos Gutierrez, Simon Lloyd, Vladislav Medvedev, Benito Pires, Evgeny Zhuzhoma. Transitive circle exchange transformations with flips. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 251-263. doi: 10.3934/dcds.2010.26.251
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[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]

Jacek Brzykcy, Krzysztof Frączek. Disjointness of interval exchange transformations from systems of probabilistic origin. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 53-73. doi: 10.3934/dcds.2010.27.53

[8]

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

[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]

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

[11]

Michael Baake, John A. G. Roberts, Reem Yassawi. Reversing and extended symmetries of shift spaces. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 835-866. doi: 10.3934/dcds.2018036

[12]

Jean-Francois Bertazzon. Symbolic approach and induction in the Heisenberg group. Discrete & Continuous Dynamical Systems - A, 2012, 32 (4) : 1209-1229. doi: 10.3934/dcds.2012.32.1209

[13]

Lyndsey Clark. The $\beta$-transformation with a hole. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1249-1269. doi: 10.3934/dcds.2016.36.1249

[14]

Giuseppe Alì, John K. Hunter. Orientation waves in a director field with rotational inertia. Kinetic & Related Models, 2009, 2 (1) : 1-37. doi: 10.3934/krm.2009.2.1

[15]

Shigeki Akiyama, Edmund Harriss. Pentagonal domain exchange. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4375-4400. doi: 10.3934/dcds.2013.33.4375

[16]

Corentin Boissy. Classification of Rauzy classes in the moduli space of Abelian and quadratic differentials. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3433-3457. doi: 10.3934/dcds.2012.32.3433

[17]

Jon Fickenscher. A combinatorial proof of the Kontsevich-Zorich-Boissy classification of Rauzy classes. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1983-2025. doi: 10.3934/dcds.2016.36.1983

[18]

Michael Baake, Natascha Neumärker, John A. G. Roberts. Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 527-553. doi: 10.3934/dcds.2013.33.527

[19]

Daniel Wilczak, Piotr Zgliczyński. Topological method for symmetric periodic orbits for maps with a reversing symmetry. Discrete & Continuous Dynamical Systems - A, 2007, 17 (3) : 629-652. doi: 10.3934/dcds.2007.17.629

[20]

Marc Chamberland, Victor H. Moll. Dynamics of the degree six Landen transformation. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 905-919. doi: 10.3934/dcds.2006.15.905

2017 Impact Factor: 1.179

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (1)

[Back to Top]