R. [. Abarbanel, J. J. Brown, L. S. Sidorowich, and . Tsimring, The analysis of observed chaotic data in physical systems, Reviews of Modern Physics, vol.65, issue.4, pp.1331-1392, 1993.
DOI : 10.1103/RevModPhys.65.1331

]. M. Beca and L. Benedicks, Carleson On iterations of 1 ? ax 2 on (-1,1) Ann. of Math Transformations dilatantes de l'intervalle et théorèmes limites, pp.1-25, 1985.

]. J. Bodav, B. Bourdon, and B. Daireaux, Vallée Dynamical Analysis of a-Euclidean Algorithms, Journal of Algorithms, vol.44, issue.1, pp.246-285, 2002.

J. Buzzi, Intrinsic ergodicity of affine maps in [0, 1] d, Monatshefte f???r Mathematik, vol.76, issue.2, pp.97-118, 1997.
DOI : 10.1007/BF01300614

]. J. Bu2, Buzzi Markov extensions for multi-dimensional dynamical systems, Israel J. Math, vol.112, pp.357-380, 1999.

]. J. Bu3 and . Buzzi, Absolutely continuous invariant measures for generic piecewise affine and expanding maps Buzzi Thermodynamical formalism for picewise invertible maps : absolutely continuous invariant measures as equilibrium states in Smooth Ergodic Theory and its Applications, Proceedings of Symposia in Pure Mathematics 69, pp.1743-1750, 1999.

]. J. Bu5, Buzzi Absolutely continuous invariant probability measures for arbitrary expanding piecewise R-analytic mappings of the plane. Ergodic Theory Dynam, Systems, vol.20, pp.697-708, 2000.

J. Buzzi and V. , Maume-Deschamps Decay of correlations on towers for potentials with summable variation, Discrete and Continuous Dynamical Systems, pp.639-656, 2005.

J. Buzzi and V. , Decay of correlations for piecewise invertible maps in higher dimensions, Israel Journal of Mathematics, vol.110, issue.1, pp.203-220, 2002.
DOI : 10.1007/BF02785858

J. Buzzi, F. Paccaut, and B. Schmitt, Conformal measures for multidimensional piecewise invertible maps. Ergodic Theory Dynam, Systems, vol.21, issue.4, pp.1035-1049, 2001.

]. P. Col and . Collet, Some ergodic properties of maps of the interval Dynamical systems (Temuco, Travaux en Cours, vol.52, pp.55-91, 1991.

]. P. Cmars, S. Collet, B. Martinez, and . Schmitt, Exponential inequalities for dynamical measures of expanding maps of the interval. Probab. Theory Related Fields Piecewise smooth expanding maps in R d, Cow] W. Cowieson, pp.301-322, 2002.

]. J. Dedo, P. Dedecker, and . Doukhan, A new covariance inequality and applications. Stochastic Process, Appl, vol.106, issue.1, pp.63-80, 2003.

. M. Dgs, C. Denker, K. Grillenberger, ]. J. Dep, C. Dedecker et al., Sygmund Ergodic theory on compact spaces Lecture notes in mathematics 527 New dependence coefficients. Examples and applications to statistics Louhichi, m A new weak dependence condition and applications to moment inequalities. Stochastic Process, Appl, vol.84, issue.2, pp.313-342, 1976.

P. [. Ferraty and . Vieu, Nonparametric models for functional data, with application in regression, time series prediction and curve discrimination, Journal of Nonparametric Statistics, vol.31, issue.1-2, pp.111-125, 2004.
DOI : 10.2307/1269658

]. P. Gobo and A. Góra, Boyarsky Absolutely continuous invariant measures for piecewise expanding C 2 transformation in R N, Israel J. Math, vol.67, pp.272-286, 1989.

]. G. Keno and T. Keller, Nowicki Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps, Comm. Math. Phys, vol.149, issue.1, pp.31-69, 1992.

]. C. Li and . Liverani, Decay of correlations for piecewise expanding maps, J. Statist. Phys, vol.78, pp.3-4, 1995.

]. C. Lisv, B. Liverani, S. Saussol, and . Vaienti, Conformal measure and decay of correlation for covering weighted systems. Ergodic Theory Dynam, Systems, vol.18, issue.6, pp.1399-1420, 1998.

]. J. Mae, Maes Estimation non paramétrique pour des processus dynamiques dilatants, C. R. Acad. Sci. Paris Sér. I Math, vol.330, issue.9, pp.831-834, 2000.

]. M. Ts1 and . Tsujii, Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane, Comm. Math. Phys, vol.208, pp.605-622, 2000.

]. M. Ts2 and . Tsujii, Absolutely continuous invariant measures for expanding piecewise linear maps Invent, Math

]. M. Ts3 and . Tsujii, Piecewise Expanding maps on the plane with singular ergodic properties, Ergod. th. and Dynam. Syst