Nonlinearity 29 (2016) 2941-2960.
Georg Gottwald and Ian Melbourne
Abstract
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for
observables of compact group extensions of nonuniformly expanding maps.
In particular, our results include situations where the central limit theorem
would fail, and anomalous behaviour would prevail, if the compact group were not present. This has important consequences
for systems with noncompact Euclidean symmetry.