Exponential decay of correlations for a real-valued dynamical system embedded in R2

被引:2
作者
Jager, Lisette [1 ]
Maes, Jules [1 ]
Ninet, Alain [1 ]
机构
[1] Univ Reims, Math Lab, FR CNRS 3399, EA 4535, F-51687 Reims, France
关键词
MULTIDIMENSIONAL EXPANDING MAPS; INVARIANT-MEASURES; RECURRENCE TIMES; RATES;
D O I
10.1016/j.crma.2015.07.015
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the real valued process {X-t, t is an element of N} defined by Xt+2 = phi(X-t, Xt+1), where the X-t are bounded. We aim at proving the decay of correlations for this model, under regularity assumptions on the transformation phi. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:1041 / 1045
页数:5
相关论文
共 10 条
[1]   From rates of mixing to recurrence times via large deviations [J].
Alves, Jose F. ;
Freitas, Jorge M. ;
Luzzatto, Stefano ;
Vaienti, Sandro .
ADVANCES IN MATHEMATICS, 2011, 228 (02) :1203-1236
[2]  
[Anonymous], 1990, OXFORD STAT SCI SERI
[3]  
[Anonymous], ACTA MATH APPL SINIC
[4]  
[Anonymous], 2006, Theoretical and Mathematical Physics
[5]   ERGODIC PROPERTIES OF INVARIANT-MEASURES FOR PIECEWISE MONOTONIC TRANSFORMATIONS [J].
HOFBAUER, F ;
KELLER, G .
MATHEMATISCHE ZEITSCHRIFT, 1982, 180 (01) :119-140
[6]  
Lasota A., 1998, Chaos, fractals and noise: stochastic aspects of dynamics
[7]   Multidimensional expanding maps with singularities: a pedestrian approach [J].
Liverani, Carlangelo .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2013, 33 :168-182
[8]   Absolutely continuous invariant measures for multidimensional expanding maps [J].
Saussol, B .
ISRAEL JOURNAL OF MATHEMATICS, 2000, 116 (1) :223-248
[9]   THEORIE ERGODIQUE POUR DES CLASSES DOPERATIONS NON COMPLETEMENT CONTINUES [J].
TULCEA, CTI ;
MARINESCU, G .
ANNALS OF MATHEMATICS, 1950, 52 (01) :140-147
[10]   Recurrence times and rates of mixing [J].
Young, LS .
ISRAEL JOURNAL OF MATHEMATICS, 1999, 110 (1) :153-188