FEIGENBAUM’S CONSTANT FOR MEROMORPHIC FUNCTIONS

Jason A.C. Gallas
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Jason A.C. Gallas: Höchstleistungsrechenzentrum (HLRZ), KFA, W-5170 Jülich, Germany

International Journal of Modern Physics C (IJMPC), 1992, vol. 03, issue 03, 553-560

Abstract: We calculate Feigenbaum’s constant for a double-periodic meromorphic function: the Jacobian elliptic functionsn[2K (m)x, m].Form=0this function reduces to sin(πx), with real period, while form=1it reduces to a hyperbolic tangent, having a pure imaginary period. For intermediary m values it is unimodal but with a non-quadratic m-dependent maximum. The bifurcation tree forsn[2K(m)x, m], although very much compressed in [0, 1], presentsδ=4.699… for all values ofm.

Keywords: Feigenbaum’s Constant; Meromorphic Functions; Meromorphic Maps (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1142/S012918319200035X

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