On mixing properties of compact group extensions of hyperbolic systems

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Statistical limit theorems for suspension flows (2004, background): “4 Provided r and φ are smooth enough, the CLT (and its functional version) hold for suspension flows over the G-extensions considered in [10].”
Limit theorems for partially hyperbolic systems (2003, unknown): “Compact skew extensions are studied in [11, 12, 15, 26].”
Chapter 2 – Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics (2006, methodology): “We refer the reader to the works by Kowalski [149], Dolgopyat [76], Parry and Pollicott [192], Field, Melbourne & Török [88], and references therein.”
On differentiability of SRB states for partially hyperbolic systems (2004, background): “By [20] a generic extension is rapidly mixing.”
Random walks in compact groups (2012, methodology): “We say that a profinite group G is (c, α)-quasirandom if for every irreducible unitary representation π of G, we have dimπ ≥ c[G : Ker(π)]α.”
Averaging and Invariant Measures (2005, unknown): “Hence rapid mixing ([16]) suffices here.”