# 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}
}
• M. Feigenbaum
• Published 1 July 1978
• Mathematics
• Journal of Statistical Physics
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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