J. Aaronson and M. Denker, Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps, Stoch. Dyn, vol.1, issue.2, pp.193-237, 2001.

I. Berkes, W. Liu, and W. Wu, Komlós-Major-Tusnády approximation under dependence, Ann. Probab, vol.42, pp.794-817, 2014.

C. Cuny, J. Dedecker, and F. Merlevède, On the Komlós, Major and Tusnády strong approximation for some classes of random iterates, Stochastic Process. Appl, vol.128, issue.4, pp.1347-1385, 2018.

C. Cuny and F. Merlevède, Strong invariance principles with rate for "reverse" martingales and applications, J. Theoret. Probab, pp.137-183, 2015.

P. Erd?-os and A. Rényi, On Cantor's series with convergent 1/q n, Ann. Univ. Sci

, Budapest. Eötvös. Sect. Math, vol.2, pp.93-109, 1959.

S. Gouëzel, Sharp polynomial estimates for the decay of correlations, Israel J. Math, vol.139, pp.29-65, 2004.

S. Gouëzel, Vitesse de décorrélation et théorèmes limites pour les applications non uniformément dilatantes, 2004.

S. Gouëzel, A Borel-Cantelli lemma for intermittent interval maps, Nonlinearity, vol.20, pp.1491-1497, 2007.

D. L. Hanson and R. P. Russo, Some results on increments of the Wiener process with applications to lag sums of i.i.d. random variables, Ann. Probab, vol.11, issue.3, pp.609-623, 1983.

M. Holland, Slowly mixing systems and intermittency maps, Ergodic Theory Dynam, Systems, vol.25, pp.133-159, 2005.

H. Hu, Decay of correlations for piecewise smooth maps with indifferent fixed points, Ergodic Theory Dynam. Systems, vol.24, pp.495-524, 2004.

J. Komlós, P. Major, and G. Tusnády, An approximation of partial sums of independent RV'-s and the sample DF. I; II, Z. Wahrscheinlichkeitstheor. verw. Geb, vol.32, pp.34-58, 1975.

A. Korepanov, Equidistribution for nonuniformly expanding systems, Comm. Math. Phys, vol.359, pp.1123-1138, 2018.

A. Korepanov, Rates in almost sure invariance principle for dynamical systems with some hyperbolicity, Comm. Math. Phys, vol.363, pp.173-190, 2018.

A. Korepanov, Z. Kosloff, and I. Melbourne, Martingale-coboundary decomposition for families of dynamical systems, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.35, pp.859-885, 2018.

T. , On Coupling of Discrete Renewal Processes, Z. Wahrscheinlichkeitstheorie verw, Gebiete, vol.48, pp.57-70, 1979.

C. Liverani, B. Saussol, and S. Vaienti, A probabilistic approach to intermittency, Ergodic Theory Dynam, Systems, vol.19, pp.671-685, 1999.

I. Melbourne and M. Nicol, Almost sure invariance principle for nonuniformly hyperbolic systems, Comm. Math. Phys, vol.260, pp.131-146, 2005.

I. Melbourne and M. Nicol, A vector-valued almost sure invariance principle for hyperbolic dynamical systems, Ann. Probab, pp.478-505, 2009.

F. Merlevède and E. Rio, Strong approximation of partial sums under dependence conditions with application to dynamical systems, Stochastic Process. Appl, vol.122, pp.386-417, 2012.

Y. Pomeau and P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems, Comm. Math. Phys, vol.74, pp.189-197, 1980.

W. Philipp and W. F. Stout, Almost sure invariance principle for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc, p.161, 1975.

E. Rio, Théorie asymptotique des processus aléatoires faiblement dépendants, Math. Appl. (Berlin), p.31, 2000.

A. I. Sakhanenko, Estimates in the invariance principle in terms of truncated power moments, Sib. Math. J, vol.47, pp.1355-1371, 2006.

O. Sarig, Subexponential decay of correlations, Invent. Math, vol.150, pp.629-653, 2002.

L. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math, vol.147, pp.585-650, 1998.

L. Young, Recurrence times and rates of mixing, Israel J. Math, vol.110, pp.153-188, 1999.

R. Zweimüller, Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points, Nonlinearity, vol.11, pp.1263-1276, 1998.

R. Zweimüller, Measure preserving transformations similar to Markov shifts, Israel J. Math, vol.173, pp.421-443, 2009.