Dynamics in interacting scalar-torsion theory

In a spatially flat \ Friedmann--Lema\^{\i}tre--Robertson--Walker background space we consider a scalar-torsion gravitational model which has similar properties with the dilaton theory. This teleparallel model is invariant under a discrete transformation similar to the Gasperini-Veneziano duality transformation. Moreover, in the gravitational Action integral we introduce the Lagrangian function of a pressureless fluid source which is coupled to the teleparallel dilaton field. This specific gravitational theory with interaction in the dark sector of the universe is investigated by using methods of the dynamical system analysis. We calculate that the theory provides various areas of special interest for the evolution of the cosmological history. Inflationary scaling solutions and the de Sitter universe is recovered. Furthermore, we calculate that there exist an attractor which provides a stable solution where the two fluid components, the scalar field and the pressureless matter, contribute in the cosmological fluid. This solution is of special interest because it can describe the present epoch. Finally, the qualitative evolution of the cosmographic parameters is discussed.