  The strong longitudinal expansion characteristic of heavy-ion collisions
leads to universal attractor behaviour of the resulting drop of Quark-Gluon
Plasma already at very early times. Assuming approximate boost invariance, we
incorporate transverse dynamics of this system by linearizing the
Mueller-Israel-Stewart theory around the attractor. The result is a system of
coupled ordinary differential equations which describe the proper-time
evolution of Fourier modes encoding the transverse structure of the initial
energy deposition. The late time asymptotic behaviour of solutions is described
by transseries which make manifest the stability of the attractor against
transverse perturbations. In this framework, most of the physically relevant
information resides in the exponentially suppressed corrections to evolution
along the attractor, which are not yet negligible at freeze-out. These findings
also suggest a simple numerical approach to QGP dynamics which accounts for the
transverse dynamics using a finite number of Fourier modes. We show that this
approach is able to describe collectivity at the level of the transverse
anisotropy, as a surrogate for elliptic flow. Physical observables can be
expressed in terms of the asymptotic data evaluated at freeze-out, which we
illustrate by calculating the final multiplicity distributions.
