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Phys. 215, 119–142 (2000) 16. : Prescribing Gaussian Curvature on S 2 . Acta Math. 159, 214–259 (1987) 17. : Scalar curvatures on S 2 . Trans. AMS 303, 365–382 (1987) 18. : Prescribing Gaussian curvature on surfaces with conical singularities. J. Geom. Anal. 1, 359–372 (1991) 19. : Classification of solutions of some nonlinear elliptic equations. Duke Math. J. 63 (3), 615–622 (1991) 20. : Qualitative properties of solutions to some nonlinear elliptic equations in R2 . Duke Math. J. 71 (2), 427–439 (1993) 21.

Floquet Theory for Partial Differential Equations. : Absence of singular spectrum for a perturbation of a two-dimensional Laplace–Beltrami operator with periodic electo–magnetic potential. J. Phys. A: Math. Gen. : Absolute continuity of the periodic magnetic Schrödinger operator. : Time Dependent Approach to Scattering from Impurities in a Crystal. Commun. Math. Phys. 33, 335–343 (1973) Communicated by P. Sarnak Commun. Math. Phys. 1007/s00220-002-0676-5 Communications in Mathematical Physics Central Limit Theorems and Invariance Principles for Time-One Maps of Hyperbolic Flows Ian Melbourne1 , Andrei Török2,3 1 Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH, UK.

The suspension (semi)-flow is given by Tt (x, s) = (x, s + t) and the invariant measure µr = µ × / r dµ is an equilibrium measure for the flow, where is Lebesgue measure on R. Define the space Fθ (Xr+ ) consisting of continuous functions φ : Xr+ → R that are Lipschitz with respect to the metric dθ (x, x ) + |s − s | on X + × R restricted to {(x, s) ∈ X+ × R : 0 ≤ s ≤ r(x)}. Note that the functions in Fθ (Xr+ ) are continuous along the flow direction. Let Fk,θ (Xr+ ) consist of functions φ that are C k in the flow direction j such that ∂t φ ∈ Fθ (Xr+ ) for j = 0, 1, .