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A continuum model of mean field coupled circle maps Balint, Peter


We consider a model of globally coupled circle maps, the finite version of which was studied in the works of Koiller-Young, Fernandez and Balint-Selley. In the continuum version the state of the system is described by a density on the circle. For a fairly general class of expanding circle maps we show that, for sufficiently small coupling, there is a unique invariant density. For sufficiently strong coupling the density converges to a Dirac mass that moves chaotically on the circle. This is joint work with G. Keller, F. Selley and I.P. Toth.

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