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It is shown rigorously in this paper that an elementary 3-D quadratic map- ping is superstable, i.e. it is superstable for some ranges o f its bifurcation parameters. Numerical results that confirm the theory are also given and d iscussed. These numer- ical results give a new route to chaos which we call: the superstable quasi-periodic route to chaos.

An example of superstable quadratic mapping of the space