Foundations of ghost stability

We present a new method to analytically prove global stability in ghost-ridden dynamical systems. Our proposal encompasses all prior results and consequentially extends them. In particular, we show that stability can follow from a conserved quantity that is unbounded from below, contrary to expectation. Novel examples illustrate all our results. Our findings take root on a careful examination of the literature, here comprehensively reviewed for the first time. This work lays the mathematical basis for ulterior extensions to field theory and quantization, and it constitutes a gateway for inter-disciplinary research in dynamics and integrability.