A note on the evaluation of Feigenbaum's δs via a direct method

M McCartney

A note on the evaluation of Feigenbaum's δs via a direct method

M McCartney

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Abstract

We calculate, via the location of superstable orbits, Feigenbaum’s δ for maps with a single maximum of order √ 2 ≤β≤10 . Estimates are found using orbits of up to period 2 32 . Results are presented for integer βand β= √ 2 , √ 3 , e, π, φ, φ 2 and φ 3 . A discrepancy between the results presented and the results of previous work for odd values of βis noted.

Original language	English
Article number	105328
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	90
Issue number	2020
Early online date	21 May 2020
Publication status	Published (in print/issue) - 1 Nov 2020

UN SDGs

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SDG 9 Industry, Innovation, and Infrastructure

Keywords

Discrete Chaos
Feigenbaum Constants
Period Doubling

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feigenbaum specrtrum paper-repository-versionAuthor Accepted Manuscript, 123 KBLicence: CC BY-NC-ND

Cite this

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N2 - We calculate, via the location of superstable orbits, Feigenbaum’s δ for maps with a single maximum of order √ 2 ≤β≤10 . Estimates are found using orbits of up to period 2 32 . Results are presented for integer βand β= √ 2 , √ 3 , e, π, φ, φ 2 and φ 3 . A discrepancy between the results presented and the results of previous work for odd values of βis noted.

AB - We calculate, via the location of superstable orbits, Feigenbaum’s δ for maps with a single maximum of order √ 2 ≤β≤10 . Estimates are found using orbits of up to period 2 32 . Results are presented for integer βand β= √ 2 , √ 3 , e, π, φ, φ 2 and φ 3 . A discrepancy between the results presented and the results of previous work for odd values of βis noted.

KW - Discrete Chaos

KW - Feigenbaum Constants

KW - Period Doubling

UR - https://www.scopus.com/pages/publications/85085275200

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SN - 1007-5704

VL - 90

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 2020

M1 - 105328

ER -

A note on the evaluation of Feigenbaum's δs via a direct method

Abstract

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Keywords

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