Experimental Mathematics

Feigenbaum numbers for certain flat-top families

Hans Thunberg

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 $\delta$.

Article information

Source
Experiment. Math., Volume 3, Issue 1 (1994), 51-57.

Dates
First available in Project Euclid: 3 September 2003

https://projecteuclid.org/euclid.em/1062621003

Mathematical Reviews number (MathSciNet)
MR1302818

Zentralblatt MATH identifier
0807.58035

Subjects
Primary: 58F08
Secondary: 39B12: Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]

Citation

Thunberg, Hans. Feigenbaum numbers for certain flat-top families. Experiment. Math. 3 (1994), no. 1, 51--57. https://projecteuclid.org/euclid.em/1062621003