American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Necessary and sufficient conditions for existence of solutions of a variational problem involving the curl
  • DCDS Home
  • This Issue
  • Next Article
    Global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems
January  2005, 12(1): 79-96. doi: 10.3934/dcds.2005.12.79

Statistical properties of compact group extensions of hyperbolic flows and their time one maps

Michael Field 1, , Ian Melbourne 2, , Matthew Nicol 1, and  Andrei Török 1,

1. 

Department of Mathematics, University of Houston, Houston, TX 77204-3008, United States, United States
2. 

Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom

Received  July 2003 Revised  July 2004 Published  December 2004

Recent work of Dolgopyat shows that "typical" hyperbolic flows exhibit rapid decay of correlations. Melbourne and Török used this result to derive statistical limit laws such as the central limit theorem and the almost sure invariance principle for the time-one map of such flows.
In this paper, we extend these results to equivariant observations on compact group extensions of hyperbolic flows and their time one maps.
Keywords: decay of correlations, almost sure invariance principle, hyperbolic flow, axiom A., Compact group extensions.
Mathematics Subject Classification: 37A25, 37A50, 37D20, 37C8.
Citation: Michael Field, Ian Melbourne, Matthew Nicol, Andrei Török. Statistical properties of compact group extensions of hyperbolic flows and their time one maps. Discrete & Continuous Dynamical Systems, 2005, 12 (1) : 79-96. doi: 10.3934/dcds.2005.12.79
[1]

Yaofeng Su. Almost surely invariance principle for non-stationary and random intermittent dynamical systems. Discrete & Continuous Dynamical Systems, 2019, 39 (11) : 6585-6597. doi: 10.3934/dcds.2019286
[2]

Viorel Niţică. Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups. Discrete & Continuous Dynamical Systems, 2011, 29 (3) : 1197-1204. doi: 10.3934/dcds.2011.29.1197
[3]

Zvi Artstein. Invariance principle in the singular perturbations limit. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3653-3666. doi: 10.3934/dcdsb.2018309
[4]

Michiko Yuri. Polynomial decay of correlations for intermittent sofic systems. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 445-464. doi: 10.3934/dcds.2008.22.445
[5]

Vincent Lynch. Decay of correlations for non-Hölder observables. Discrete & Continuous Dynamical Systems, 2006, 16 (1) : 19-46. doi: 10.3934/dcds.2006.16.19
[6]

Ioannis Konstantoulas. Effective decay of multiple correlations in semidirect product actions. Journal of Modern Dynamics, 2016, 10: 81-111. doi: 10.3934/jmd.2016.10.81
[7]

Alexei Kaltchenko, Nina Timofeeva. Entropy estimators with almost sure convergence and an O(n-1) variance. Advances in Mathematics of Communications, 2008, 2 (1) : 1-13. doi: 10.3934/amc.2008.2.1
[8]

Wensheng Yin, Jinde Cao. Almost sure exponential stabilization and suppression by periodically intermittent stochastic perturbation with jumps. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4493-4513. doi: 10.3934/dcdsb.2020109
[9]

Alexandra Rodkina, Henri Schurz, Leonid Shaikhet. Almost sure stability of some stochastic dynamical systems with memory. Discrete & Continuous Dynamical Systems, 2008, 21 (2) : 571-593. doi: 10.3934/dcds.2008.21.571
[10]

Adriano Da Silva, Christoph Kawan. Invariance entropy of hyperbolic control sets. Discrete & Continuous Dynamical Systems, 2016, 36 (1) : 97-136. doi: 10.3934/dcds.2016.36.97
[11]

Lorenzo J. Díaz, Todd Fisher. Symbolic extensions and partially hyperbolic diffeomorphisms. Discrete & Continuous Dynamical Systems, 2011, 29 (4) : 1419-1441. doi: 10.3934/dcds.2011.29.1419
[12]

Mahesh Nerurkar. Forced linear oscillators and the dynamics of Euclidean group extensions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 1201-1234. doi: 10.3934/dcdss.2016049
[13]

Stefano Galatolo, Pietro Peterlongo. Long hitting time, slow decay of correlations and arithmetical properties. Discrete & Continuous Dynamical Systems, 2010, 27 (1) : 185-204. doi: 10.3934/dcds.2010.27.185
[14]

Justin Forlano. Almost sure global well posedness for the BBM equation with infinite $ L^{2} $ initial data. Discrete & Continuous Dynamical Systems, 2020, 40 (1) : 267-318. doi: 10.3934/dcds.2020011
[15]

Jingrui Wang, Keyan Wang. Almost sure existence of global weak solutions to the 3D incompressible Navier-Stokes equation. Discrete & Continuous Dynamical Systems, 2017, 37 (9) : 5003-5019. doi: 10.3934/dcds.2017215
[16]

Takahisa Inui. Global dynamics of solutions with group invariance for the nonlinear schrödinger equation. Communications on Pure & Applied Analysis, 2017, 16 (2) : 557-590. doi: 10.3934/cpaa.2017028
[17]

Dariusz Skrenty. Absolutely continuous spectrum of some group extensions of Gaussian actions. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 365-378. doi: 10.3934/dcds.2010.26.365
[18]

David Ralston, Serge Troubetzkoy. Ergodic infinite group extensions of geodesic flows on translation surfaces. Journal of Modern Dynamics, 2012, 6 (4) : 477-497. doi: 10.3934/jmd.2012.6.477
[19]

Karla Díaz-Ordaz. Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenz-like maps. Discrete & Continuous Dynamical Systems, 2006, 15 (1) : 159-176. doi: 10.3934/dcds.2006.15.159
[20]

Jérôme Buzzi, Véronique Maume-Deschamps. Decay of correlations on towers with non-Hölder Jacobian and non-exponential return time. Discrete & Continuous Dynamical Systems, 2005, 12 (4) : 639-656. doi: 10.3934/dcds.2005.12.639

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (46)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy