C3S2
The Clarkson Center for Complex Systems Science
Robert Corless, Editor-in-Chief, Maple Transactions
Will present a talk titled:
“A Fractal Eigenvector”
Abstract: 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=z2k−1+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.
SC166
January 27, 2023
12:00 pm
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C3S2 Clarkson Center for Complex Systems Science l http://webspace.clarkson.edu/~ebollt/Website-C3S2/index.html
CLARKSON UNIVERSITY l Potsdam, New York 13699-5720
