  Thermal convection in an inclined layer between two parallel walls kept at
different fixed temperatures is studied for fixed Prandtl number Pr=1.07.
Depending on the angle of inclination and the imposed temperature difference,
the flow exhibits a large variety of self-organized spatio-temporal convection
patterns. Close to onset, these patterns have been explained in terms of linear
stability analysis of primary and secondary flow states. At larger temperature
difference, far beyond onset, experiments and simulations show complex,
dynamically evolving patterns that are not described by stability analysis and
remain to be explained. Here we employ a dynamical systems approach. We
construct stable and unstable exact invariant states, including equilibria and
periodic orbits of the fully nonlinear three-dimensional Oberbeck-Boussinesq
equations. These invariant states underlie the observed convection patterns
beyond their onset. We identify state-space trajectories that, starting from
the unstable laminar flow, follow a sequence of dynamical connections between
unstable invariant states until the dynamics approaches a stable attractor.
Together, the network of dynamically connected invariant states mediates
temporal transitions between coexisting invariant states and thereby supports
the observed complex time-dependent dynamics in inclined layer convection.
