[#P11200] Is the Feigenbaum delta constant transcendental?
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Problem. For 0 <= mu <= 2, let \(f_mu\)(x)=1-mu*x^2. In its principal period-doubling cascade, let mu_n be the parameter at which the attracting cycle of least period 2^(n-1) has multiplier -1 and bifurcates to a cycle of period 2^n. Define delta=lim_{n->infinity}(mu_(n+1)-mu_n)/(mu_(n+2)-mu_(n+1)), the Feigenbaum delta constant. Is delta transcendental over the rational numbers?
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2See also
- Hilbert's sixteenth problem, second partdynamical systems
- Birkhoff conjecture for integrable convex billiardsdynamical systems
- Persistent exponential stretching of a material line in two-dimensional Euler flowdynamical systems
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“Is the Feigenbaum delta constant transcendental?.” TheoremDB. P11200. Problem statement; statement identity tdbc1:7b0ef1298f03ae5413d2495f161cc15142c600d8ea243ecaaeec55e664f50271; statement text SHA-256 c4609340c120c6e3da8afa7daac9e54c1aee99fefda72990b1e7e261c7ba5fa0. https://theoremdb.org/statement/?ref=P11200
@misc{theoremdb-problem-c4609340c120c6e3da8afa7daac9e54c1aee99fefda72990b1e7e261c7ba5fa0,
title = {{Is the Feigenbaum delta constant transcendental?}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:7b0ef1298f03ae5413d2495f161cc15142c600d8ea243ecaaeec55e664f50271; statement text SHA-256 c4609340c120c6e3da8afa7daac9e54c1aee99fefda72990b1e7e261c7ba5fa0},
url = {https://theoremdb.org/statement/?ref=P11200}
}Plain text: Built Markdown snapshot
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