Dynamical systems approach and generic properties of $f(T)$ cosmology

We present a systematic analysis of the dynamics of flat Friedmann-Lema\^{i}tre-Robertson-Walker cosmological models with radiation and dust matter in generalized teleparallel $f(T)$ gravity. We show that the cosmological dynamics of this model is fully described by a function $W(H)$ of the Hubble parameter, which is constructed from the function $f(T)$. After reducing the phase space to two dimensions we derive the conditions on $W(H)$ for the occurrence of de Sitter fixed points, accelerated expansion, crossing the phantom divide, and finite time singularities. Depending on the model parameters it is possible to have a bounce (from contraction to expansion) or a turnaround (from expansion to contraction), but cyclic or oscillating scenarios are prohibited. As an illustration of the formalism we consider power law $f(T) = T + \alpha(-T)^n$ models, and show that these allow only one period of acceleration and no phantom divide crossing.