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1994 Feigenbaum numbers for certain flat-top families
Hans Thunberg
Experiment. Math. 3(1): 51-57 (1994).

Abstract

We report on numerical results for certain families of S-unimodal maps with flat critical point. For four one-parameter families, differing in their amount of flatness, we study the Feigenbaum limits $\alpha$ and $\delta$. There seems to be a finite $\delta$ and a finite $\alpha$ associated with each period doubling cascade in each family. Some rough numerical estimates are obtained, and our upper bound on $\delta$ is smaller than the corresponding supremum for families with nonflat critical point. One would expect that these numbers should only depend on the nature (flatness) of the maximum, and thus be constant in each family. Our data support this hypothesis for $\alpha$, but are inconclusive when it comes to $\delta$.

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Hans Thunberg. "Feigenbaum numbers for certain flat-top families." Experiment. Math. 3 (1) 51 - 57, 1994.

Information

Published: 1994
First available in Project Euclid: 3 September 2003

zbMATH: 0807.58035
MathSciNet: MR1302818

Subjects:
Primary: 58F08
Secondary: 39B12

Rights: Copyright © 1994 A K Peters, Ltd.

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Vol.3 • No. 1 • 1994
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