July  2008, 2(3): 457-464. doi: 10.3934/jmd.2008.2.457

Hausdorff dimension for ergodic measures of interval exchange transformations

1. 

Department of Mathematics, Rice University, Houston, TX 77005, United States

Received  November 2007 Published  April 2008

We show that there exist minimal interval-exchange transformations with an ergodic measure whose Hausdorff dimension is arbitrarily small, even 0. We will also show that in particular cases one can bound the Hausdorff dimension between $\frac{1}{2r+4}$ and $\frac{1}{r}$ for any r greater than 1.
Citation: 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
[1]

Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $ \beta $-transformation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 525-536. doi: 10.3934/dcds.2020267

[2]

Sergio Zamora. Tori can't collapse to an interval. Electronic Research Archive, , () : -. doi: 10.3934/era.2021005

[3]

Meihua Dong, Keonhee Lee, Carlos Morales. Gromov-Hausdorff stability for group actions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1347-1357. doi: 10.3934/dcds.2020320

[4]

Andy Hammerlindl, Jana Rodriguez Hertz, Raúl Ures. Ergodicity and partial hyperbolicity on Seifert manifolds. Journal of Modern Dynamics, 2020, 0: 331-348. doi: 10.3934/jmd.2020012

[5]

Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299

[6]

Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103

[7]

Guojie Zheng, Dihong Xu, Taige Wang. A unique continuation property for a class of parabolic differential inequalities in a bounded domain. Communications on Pure & Applied Analysis, 2021, 20 (2) : 547-558. doi: 10.3934/cpaa.2020280

[8]

Harrison Bray. Ergodicity of Bowen–Margulis measure for the Benoist 3-manifolds. Journal of Modern Dynamics, 2020, 16: 305-329. doi: 10.3934/jmd.2020011

[9]

Andreu Ferré Moragues. Properties of multicorrelation sequences and large returns under some ergodicity assumptions. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020386

[10]

Shang Wu, Pengfei Xu, Jianhua Huang, Wei Yan. Ergodicity of stochastic damped Ostrovsky equation driven by white noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1615-1626. doi: 10.3934/dcdsb.2020175

[11]

Tomáš Oberhuber, Tomáš Dytrych, Kristina D. Launey, Daniel Langr, Jerry P. Draayer. Transformation of a Nucleon-Nucleon potential operator into its SU(3) tensor form using GPUs. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1111-1122. doi: 10.3934/dcdss.2020383

[12]

Hua Qiu, Zheng-An Yao. The regularized Boussinesq equations with partial dissipations in dimension two. Electronic Research Archive, 2020, 28 (4) : 1375-1393. doi: 10.3934/era.2020073

[13]

Lisa Hernandez Lucas. Properties of sets of Subspaces with Constant Intersection Dimension. Advances in Mathematics of Communications, 2021, 15 (1) : 191-206. doi: 10.3934/amc.2020052

[14]

Russell Ricks. The unique measure of maximal entropy for a compact rank one locally CAT(0) space. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 507-523. doi: 10.3934/dcds.2020266

[15]

Yuanshi Wang. Asymmetric diffusion in a two-patch mutualism system characterizing exchange of resource for resource. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 963-985. doi: 10.3934/dcdsb.2020149

[16]

João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138

[17]

Sabira El Khalfaoui, Gábor P. Nagy. On the dimension of the subfield subcodes of 1-point Hermitian codes. Advances in Mathematics of Communications, 2021, 15 (2) : 219-226. doi: 10.3934/amc.2020054

[18]

Annegret Glitzky, Matthias Liero, Grigor Nika. Dimension reduction of thermistor models for large-area organic light-emitting diodes. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020460

[19]

Norman Noguera, Ademir Pastor. Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021018

[20]

Fang Li, Bo You. On the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021024

2019 Impact Factor: 0.465

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]