Area-preserving nontwist maps, i.e. maps that violate the twist condition, arise in the study of degenerate Hamiltonian systems for which the standard version of the KAM theorem fails to apply. These maps have found applications in several areas including plasma physics, fluid mechanics, and condensed matter physics. Previous work has limited attention to maps in 2-dimensional phase space. Going beyond these studies, in this paper we study nontwist maps with many-degrees-offreedom. We propose a

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... model in which the different degrees of freedom are coupled through a mean-field that evolves self-consistently. Based on the linear stability of period-one and periodtwo orbits of the coupled maps, we construct coherent states in which the degrees of freedom are synchronized and the mean-field stays nearly fixed. Nontwist systems exhibit global bifurcations in phase space known as separatrix reconnection. Here we show that the mean-field coupling leads to dynamic, self-consistent reconnection in which transport across invariant curves can take place in the absence of chaos due to changes in the topology of the separatrices. In the context of selfconsistent chaotic transport we study two novel problems: suppression of diffusion and breakup of the shearless curve. For both problems we construct a macroscopic effective diffusion model with time-dependent diffusivity. Self-consistent transport near criticality is also studied, and it is shown that the threshold for global transport as function of time is a fat-fractal Cantor set.