Decay of correlations for piecewise smooth maps with indifferent fixed points

By Huyi Hu. Ergodic Theory and Dynamical Systems, 2004

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Large deviations for nonuniformly hyperbolic systems (2008, background): “Various authors, including [16, 20, 30, 37], have studied intermittency (Pomeau-Manneville) maps of the type T : [0, 1] → [0, 1] given by”
Markov structures and decay of correlations for non-uniformly expanding dynamical systems☆ (2002, methodology): “measure with positive Lyapunov exponent but strictly subexponential [22, 20 ,30,24] (and in some cases even subpolynomial [19]) decay of correlations.”
THE DYNAMICAL BOREL-CANTELLI LEMMA FOR INTERVAL MAPS (2007, background): “In [7], Hu showed that there exist constants C1 > 0 and & such that for any m ≥ 0 and E ∈ ξm and for any measurable set F ⊂ [2 , 1), |μ(T−n−mF ∩ E) − μ(F )μ(E)| ≤ C1m (n − &)β−1 μ(F )μ(E), for any n > &, (8) where β = 1/α.”
Operator renewal theory and mixing rates for dynamical systems with infinite measure (2010, background): “The density h is globally Lipschitz on (ǫ, 1] for any ǫ > 0 (see for example [25] or [31, Lemma 2.”
Polynomial loss of memory for maps of the interval with a neutral fixed point (2014, background): “Thanks to a general theory by Hu [6], we know that the density f of the absolutely continuous invariant measure of T”