A Fractal Eigenvector

DOI10.1080/00029890.2022.2059311zbMath1491.15012arXiv2104.01116OpenAlexW4225324483MaRDI QIDQ5082412

Neil J. Calkin, Piers W. Lawrence, Eunice Y. S. Chan, Robert M. Corless, David J. Jeffrey

Publication date: 16 June 2022

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.01116

zbMATH Keywords

Perron-Frobenius theoremMandelbrot matricesMandelbrot iteration

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Fractals (28A80) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46)

Uses Software

• OEIS
• Ode15s
• na20
• SuiteSparse.GraphBLAS

Cites Work

• Perturbations of matrices: A theorem on the Perron vector and its applications to input-output models
• Design, analysis, and implementation of a multiprecision polynomial rootfinder
• Algebraic linearizations of matrix polynomials
• Initial value problems for ODEs in problem solving environments
• Solving secular and polynomial equations: a multiprecision algorithm
• Internal addresses of the Mandelbrot set and Galois groups of polynomials
• Self-interlacing polynomials
• Eigenstructure of order-one-quasiseparable matrices. Three-term and two-term recurrence relations
• Handbook of Linear Algebra
• Solving Transcendental Equations
• Galois theory of periodic orbits of rational maps
• The Galois Theory of Periodic Points of Polynomial Maps
• The Many Proofs and Applications of Perron's Theorem
• Algorithm 1000
• First-Order Perturbation Theory for Eigenvalues and Eigenvectors
• The Largest Roots of the Mandelbrot Polynomials

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