Galaxy disks evolve through angular momentum transfers between sub-components, like gas, stars, or dark matter halos, through non axi-symmetric instabilities. The speed of this evolution is boosted in presence of a large fraction of cold and dissipative gas component. When the visible matter dominates over the whole disk, angular momentum is exchanged between gas and stars only. The gas is driven towards the center by bars, stalled transiently in resonance rings, and driven further by embedded bars, which it contributes to destroy. From a small-scale molecular torus, the gas can then inflow from viscous torques, dynamical friction, or m=1 perturbations. In the weakened bar phases, multiple-speed spiral patterns can develop and help the galaxy to accrete external gas flowing from cosmic filaments. The various phases of secular evolution are illustrated by numerical simulations.
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