# Quantitative universality for a class of nonlinear transformations

@article{Feigenbaum1978QuantitativeUF, title={Quantitative universality for a class of nonlinear transformations}, author={Mitchell J. Feigenbaum}, journal={Journal of Statistical Physics}, year={1978}, volume={19}, pages={25-52} }

AbstractA large class of recursion relationsxn + 1 = λf(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum
$$\bar x$$
. With
$$f(\bar x) - f(x) \sim \left| {x - \bar x} \right|^z (for\left| {x - \bar x} \right|$$
sufficiently small),z > 1, the universal details depend only uponz. In particular, the local structure of high-order stability sets…

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