  In this work, we perform a detailed dynamical analysis for the cosmological
applications of a nonminimal torsion-matter coupled gravity. Two alternative
formalisms are proposed, which enable one to choose between the easier approach
for a given problem, and furthermore, we analyze six specific models. In
general, we extract fixed points corresponding either to dark-matter dominated,
scaling decelerated solutions, or to dark-energy dominated accelerated
solutions. Additionally, we find that there is a small parameter region in
which the model can experience the transition from the matter epoch to a
dark-energy era. These features are in agreement with the observed universe
evolution, and make the theory a successful candidate for the description of
Nature.
