American Institute of Mathematical Sciences

Advanced
February  2006, 15(1): 1-20. doi: 10.3934/dcds.2006.15.1

A survey of recent results on some statistical features of non-uniformly expanding maps

José F. Alves 1,

1. 

CMUP, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

Received  December 2004 Revised  November 2005 Published  February 2006

The aim of this paper is to present a survey of recent results on the statistical properties of non-uniformly expanding maps on finite-dimensional Riemannian manifolds. We will mostly focus on the existence of SRB measures, continuity of the SRB measure and its entropy, decay of correlations, and stochastic stability.
Keywords: stochastic stability, statistical stability, decay of correlations, SRB measure, continuity of entropy..
Mathematics Subject Classification: Primary: 37-02, Secondary: 37A25, 37A35, 37C4.
Citation: José F. Alves. A survey of recent results on some statistical features of non-uniformly expanding maps. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 1-20. doi: 10.3934/dcds.2006.15.1
[1]

Huyi Hu, Miaohua Jiang, Yunping Jiang. Infimum of the metric entropy of hyperbolic attractors with respect to the SRB measure. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 215-234. doi: 10.3934/dcds.2008.22.215
[2]

Zhiping Chen, Youpan Han. Continuity and stability of two-stage stochastic programs with quadratic continuous recourse. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 197-209. doi: 10.3934/naco.2015.5.197
[3]

Xiangfeng Yang. Stability in measure for uncertain heat equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6533-6540. doi: 10.3934/dcdsb.2019152
[4]

Rui Pacheco, Helder Vilarinho. Statistical stability for multi-substitution tiling spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4579-4594. doi: 10.3934/dcds.2013.33.4579
[5]

Michiko Yuri. Polynomial decay of correlations for intermittent sofic systems. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 445-464. doi: 10.3934/dcds.2008.22.445
[6]

Vincent Lynch. Decay of correlations for non-Hölder observables. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 19-46. doi: 10.3934/dcds.2006.16.19
[7]

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
[8]

Peidong Liu, Kening Lu. A note on partially hyperbolic attractors: Entropy conjecture and SRB measures. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 341-352. doi: 10.3934/dcds.2015.35.341
[9]

Stefano Galatolo, Pietro Peterlongo. Long hitting time, slow decay of correlations and arithmetical properties. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 185-204. doi: 10.3934/dcds.2010.27.185
[10]

Tomasz Szarek, Mariusz Urbański, Anna Zdunik. Continuity of Hausdorff measure for conformal dynamical systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4647-4692. doi: 10.3934/dcds.2013.33.4647
[11]

Yaping Wu, Niannian Yan. Stability of traveling waves for autocatalytic reaction systems with strong decay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1601-1633. doi: 10.3934/dcdsb.2017033
[12]

Junxiong Jia, Jigen Peng, Kexue Li. On the decay and stability of global solutions to the 3D inhomogeneous MHD system. Communications on Pure & Applied Analysis, 2017, 16 (3) : 745-780. doi: 10.3934/cpaa.2017036
[13]

Stefano Galatolo, Rafael Lucena. Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps. Discrete & Continuous Dynamical Systems - A, 2020, 40 (3) : 1309-1360. doi: 10.3934/dcds.2020079
[14]

Tomás Caraballo, Leonid Shaikhet. Stability of delay evolution equations with stochastic perturbations. Communications on Pure & Applied Analysis, 2014, 13 (5) : 2095-2113. doi: 10.3934/cpaa.2014.13.2095
[15]

K Najarian. On stochastic stability of dynamic neural models in presence of noise. Conference Publications, 2003, 2003 (Special) : 656-663. doi: 10.3934/proc.2003.2003.656
[16]

Miljana Jovanović, Vuk Vujović. Stability of stochastic heroin model with two distributed delays. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2020016
[17]

Denis Serre, Alexis F. Vasseur. The relative entropy method for the stability of intermediate shock waves; the rich case. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4569-4577. doi: 10.3934/dcds.2016.36.4569
[18]

Kenneth Hvistendahl Karlsen, Nils Henrik Risebro. On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1081-1104. doi: 10.3934/dcds.2003.9.1081
[19]

Xiaoming Wang. Upper semi-continuity of stationary statistical properties of dissipative systems. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 521-540. doi: 10.3934/dcds.2009.23.521
[20]

Jane Hawkins, Michael Taylor. The maximal entropy measure of Fatou boundaries. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4421-4431. doi: 10.3934/dcds.2018192

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (18)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences