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Fractal Stationary Density in Coupled Maps
Jürgen Jost and Kiran M. Kolwankar
We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter $\epsilon$ ($0 < \epsilon < 1/4$). The dynamical system considered is chaotic and unsynchronized for this range of parameter values. We find that the stationary density, restricted on the synchronization manifold, is a fractal function. We estimate the fractal dimension of the graph of this function and show that it changes continuously with the coupling parameter.