Abstract
One interesting and important property of nonlinear dynamical systems is that they can exhibit universality—behavior that is quantitatively identical for a broad class of systems. The first and most famous example of universality in a dynamical system was identified by Feigenbaum [M. J. Feigenbaum, J. Stat. Phys. 19, 25–52 (1978), 21, 669–706 (1979)] in the period-doubling route to chaos. This note presents a new derivation of Feigenbaum’s renormalization group equation, used to understand this universality. The argument, designed for incorporation into an undergraduate dynamical systems course, is simpler than those in standard textbooks.
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