The first step in exploring the properties of dynamical systems like the Earth climate is to identify the different phase space regions where the trajectories asymptotically evolve, called ‘attractors'. In a given system, multiple attractors can co-exist under the effect of the same forcing. At the boundaries of their basins of attraction, small changes produce large effects. Therefore, they are key regions for understanding the system response to perturbations. Here we prove the existence of up to five attractors in a simplified climate system where the planet is entirely covered by the ocean (aquaplanet). These attractors range from a snowball to a hot state without sea ice, and their exact number depends on the details of the coupled atmosphere–ocean–sea ice configuration. We characterise each attractor by describing the associated climate feedbacks, by using the principal component analysis, and by measuring quantities borrowed from the study of dynamical systems, namely instantaneous dimension and persistence.