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 our reasonably robust meteorological understanding of tropical cyclones, we still face outstanding challenges for their numerical simulations. 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 data sets. 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. The large dependence of hurricanes dynamical characteristics on intensity suggests the need for adaptive parametrization schemes which take into account the dependence of the cyclone’s phase, in analogy with high-dissipation intermittent events in turbulent flows.