Although the life-cycle of hurricanes is well understood, many of the underlying physical processes occur at scales below those resolved by global Hurricanes --- and more broadly tropical cyclones --- are high-impact weather phenomena whose adverse socio-economic and ecosystem impacts affect a considerable part of the global population. Despite having a reasonably robust meteorological understanding of tropical cyclones, their simulation in numerical models remains challenging. Consequently, future changes in the frequency of occurrence and intensity of tropical cyclones are still debated. Here, we diagnose possible reasons for the poor representation of tropical cyclones in numerical models, by considering the cyclones as chaotic dynamical systems. We follow 197 tropical cyclones which occurred between 2010 and 2020 in the North Atlantic using the HURDAT2 and ERA5 datasets. We measure the cyclones' instantaneous number of active degrees of freedom (local dimension) and the persistence of their sea-level pressure and potential vorticity fields. During the most intense phases of the cyclones, and specifically when cyclones reach hurricane strength, there is a collapse of degrees of freedom and an increase in persistence, hinting to the existence of an unstable fixed point of the dynamics. Hurricanes may thus be interpreted as unstable fixed points of rotational energy, and their evolution is well-captured by the potential vorticity map of the cyclone eye. In analogy with high-dissipation intermittent events in turbulent flows, this suggests strategies to improve numerical simulations of intense tropical cyclones, and specifically the need for adaptive parametrisation schemes.