MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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.


Related publications

2005 Repository Open Access
Jürgen Jost and Kiran Murlidhar Kolwankar

Fractal stationary density in coupled maps

In: Fractals in engineering : new trends in theory and applications / Jacques Lévy-Véhel... (eds.)
London : Springer, 2005. - pp. 57-64