February  2006, 15(1): 159-176. doi: 10.3934/dcds.2006.15.159

Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenz-like maps

1. 

Mathematics Department, Imperial College, 180 Queen's Gate, SW7 2AZ, London, United Kingdom

Received  October 2005 Revised  December 2005 Published  February 2006

We prove that a one-dimensional expanding Lorenz-like map admits an induced Markov structure which allows us to obtain estimates for the rates of mixing for observables with weaker regularity than Hölder.
Citation: Karla Díaz-Ordaz. Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenz-like maps. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 159-176. doi: 10.3934/dcds.2006.15.159
[1]

Youngna Choi. Attractors from one dimensional Lorenz-like maps. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 715-730. doi: 10.3934/dcds.2004.11.715

[2]

Simon Lloyd, Edson Vargas. Critical covering maps without absolutely continuous invariant probability measure. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2393-2412. doi: 10.3934/dcds.2019101

[3]

Jiu Ding, Aihui Zhou. Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 451-458. doi: 10.3934/dcds.2000.6.451

[4]

Jawad Al-Khal, Henk Bruin, Michael Jakobson. New examples of S-unimodal maps with a sigma-finite absolutely continuous invariant measure. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 35-61. doi: 10.3934/dcds.2008.22.35

[5]

Dariusz Skrenty. Absolutely continuous spectrum of some group extensions of Gaussian actions. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 365-378. doi: 10.3934/dcds.2010.26.365

[6]

Lucia D. Simonelli. Absolutely continuous spectrum for parabolic flows/maps. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 263-292. doi: 10.3934/dcds.2018013

[7]

Oliver Knill. Singular continuous spectrum and quantitative rates of weak mixing. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 33-42. doi: 10.3934/dcds.1998.4.33

[8]

Arno Berger, Roland Zweimüller. Invariant measures for general induced maps and towers. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 3885-3901. doi: 10.3934/dcds.2013.33.3885

[9]

Wael Bahsoun, Christopher Bose. Quasi-invariant measures, escape rates and the effect of the hole. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 1107-1121. doi: 10.3934/dcds.2010.27.1107

[10]

Adrian Tudorascu. On absolutely continuous curves of probabilities on the line. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 5105-5124. doi: 10.3934/dcds.2019207

[11]

Sergiĭ Kolyada, Mykola Matviichuk. On extensions of transitive maps. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 767-777. doi: 10.3934/dcds.2011.30.767

[12]

Zhi Lin, Katarína Boďová, Charles R. Doering. Models & measures of mixing & effective diffusion. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 259-274. doi: 10.3934/dcds.2010.28.259

[13]

Lidong Wang, Xiang Wang, Fengchun Lei, Heng Liu. Mixing invariant extremal distributional chaos. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6533-6538. doi: 10.3934/dcds.2016082

[14]

Michał Misiurewicz, Sonja Štimac. Lozi-like maps. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2965-2985. doi: 10.3934/dcds.2018127

[15]

Jean René Chazottes, F. Durand. Local rates of Poincaré recurrence for rotations and weak mixing. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 175-183. doi: 10.3934/dcds.2005.12.175

[16]

Yiming Ding. Renormalization and $\alpha$-limit set for expanding Lorenz maps. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 979-999. doi: 10.3934/dcds.2011.29.979

[17]

Ian Melbourne, Dalia Terhesiu. Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure. Journal of Modern Dynamics, 2018, 12: 285-313. doi: 10.3934/jmd.2018011

[18]

Oliver Jenkinson. Optimization and majorization of invariant measures. Electronic Research Announcements, 2007, 13: 1-12.

[19]

Siniša Slijepčević. Stability of invariant measures. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1345-1363. doi: 10.3934/dcds.2009.24.1345

[20]

Ralf Spatzier, Lei Yang. Exponential mixing and smooth classification of commuting expanding maps. Journal of Modern Dynamics, 2017, 11: 263-312. doi: 10.3934/jmd.2017012

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]