Year: 2022
Type: article
Abstract: The recursively-constructed family of Mandelbrot matrices Mn for n = 1, 2, … have nonnegative entries (indeed just 0 and 1, so each Mn can be called a binary matrix) and have eigenvalues whose negatives −λ=c give periodic orbits under the Mandelbrot iteration, namely zk=zk−12+c with z0=0, and are thus contained in the Mandelbrot set. By the Perron–Frobenius theorem, the matrices Mn have a dominant real positive eigenvalue, which we call ρn. This article examines the eigenvector belonging to that dominant eigenvalue and its fractal-like structure, and similarly examines (with less success) the dominant singular vectors of Mn from the singular value decomposition.
Source: American Mathematical Monthly
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3145542939