Lambert'sWfunction and convergence of infinite exponentials in the space of quaternions

DOI10.1080/17476930600772377zbMath1151.37316OpenAlexW2147943464MaRDI QIDQ3426246

I. N. Galidakis

Publication date: 8 March 2007

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930600772377

zbMATH Keywords

iterationfixed pointJulia setperiodic pointFatou setauxiliary equationinfinite exponentialpower towerLambert's \(W\) function

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Fractals (28A80) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Exponential and trigonometric functions (33B10)

Uses Software

• Maple

Cites Work

• Unnamed Item
• On the Lambert \(w\) function
• Exponentials Reiterated
• Periodic points of entire functions: proof of a conjecture of Baker
• Quaternionic analysis
• Iteration of meromorphic functions
• Iteration of Quaternion Functions
• On an application of Lambert'sWfunction to infinite exponentials
• The Quaternion Calculus
• On solving the p-th complex auxiliary equation f ^(p)(z) = z
• An Elementary Note on Powers of Quaternions
• The Roots of a Quaternion

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