A parameter ASIP for the quadratic family
Consider the quadratic family Ta(x) = ax(1-x) for x ∈ [0, 1] and mixing Collet-Eckmann (CE) parameters a ∈ (2, 4). For bounded φ, set φ˜a := φ-∫ φ dμa, with μa the unique acim of Ta, and put (σa(φ))2 := ∫ φ˜2a dμa + 2Σ i>0 ∫ phi;˜a(φ˜a o T1a) dμa. For any mixing Misiurewicz parameter a∗, we find a positive measure set Ω∗ of mixing CE parameters, containing a∗ as a Lebesgue density point, such that
