  We introduce a new approach to Gottesman-Kitaev-Preskill (GKP) states that
treats their finite-energy version in an exact manner. Based on this analysis,
we develop new qubit-oscillator circuits that autonomously stabilize a GKP
manifold, correcting errors without relying on qubit measurements. Finally, we
show numerically that logical information encoded in GKP states is very robust
against typical oscillator noise sources when stabilized by these new circuits.
