Complex dynamics of the limit periodic system \(F_ n(z)=F_{n-1}(f_ n(z))\), \(f_ n\to f\)

DOI10.1016/0377-0427(90)90420-5zbMath0724.30003OpenAlexW2050824172MaRDI QIDQ2644798

John Gill

Publication date: 1990

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(90)90420-5

zbMATH Keywords

fixed pointsMöbius transformationschaoticshadowinglimit periodic

Mathematics Subject Classification ID

Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of infinite limiting processes (40A99)

Related Items (4)

Random iterations, fixed points and invariant CRF-horospheres in complex Banach spaces ⋮ Stability of the Denjoy-Wolff theorem ⋮ Random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces ⋮ Random iterations of holomorphic maps in complex Banach spaces

Cites Work

• Accelerating convergence of limit periodic continued fractions \(K(a_n/1)\)
• Convergence properties of sequences ol linear fractional transformations
• The use of repulsive fixed points to analytically continue certain functions
• Compositions of analytic functions of the form \(F_ n(z)=F_{n-1}(f_ n(z))\), \(f_ n(z)\to f(z)\)
• Limit periodic iteration
• Numerical orbits of chaotic processes represent true orbits
• Converging Factors for Continued Fractions K(a n /1), a n →0
• Infinite Compositions of Mobius Transformations
• On convergence of sequences of linear fractional transformations
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