  Higher-order gravity models have been recently the subject of much attention
in the context of cosmic acceleration. These models are derived by adding
various curvature invariants to the Einstein-Hilbert action. Several studies
showed that these models can have late-time self-acceleration and could, in
some cases, fit various observational constraints. In view of the infinite
spectrum of invariants that could be built from curvature tensors, we propose
here a method based on minimal sets of independent invariants as a possible
route for a systematic approach to these models. We explore a connection made
between theorems on bases in invariants theory in relativity and higher-order
cosmological models. A dynamical system analysis is performed and some models
with accelerating attractors are discussed. The asymptotic behavior of the
models is also studied using analytical calculations.
