Eigenvalues in Filled Julia Sets
Document Type
Article
Department or Administrative Unit
Mathematics
Publication Date
2011
Abstract
We show how Julia sets can be introduced very naturally in a junior-level linear algebra course, as a way of exposing students to the contemporary area of complex dynamics. The standard definition of the filled Julia set of a polynomial is generalized to the setting of polynomial iteration of matrices. We prove that the eigenvalues of any matrix bounded under iteration by a polynomial must lie in the corresponding filled Julia set. A partial converse is obtained if the matrix is assumed to be diagonalizable. Still another partial converse is proven by assuming the spectrum of the matrix is contained in the interior of corresponding filled Julia set.
Recommended Citation
Fassett, J. E. (2011). Eigenvalues in Filled Julia Sets. Mathematics Magazine, 84(3), 221–227. https://doi.org/10.4169/math.mag.84.3.221
Journal
Mathematics Magazine
Copyright
© Mathematical Association of America
Comments
This article was originally published in Mathematics Magazine. The full-text article from the publisher can be found here.
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