ALGEBRAIC YUZVINSKI FORMULA Article Swipe

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Mathematics Endomorphism Topological entropy Abelian group Pure mathematics Algebraic number Entropy (arrow of time) Vector space Discrete mathematics Algebra over a field Mathematical analysis Quantum mechanics Physics

Anna Giordano Bruno , Simone Virili ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1016/j.jalgebra.2014.10.007 · OA: W2963034929

Topological entropy is very well-understood for endomorphisms of compact Abelian groups. A fundamental result in this context is the so-called Yuzvinski Formula, which is the key step in finding the topological entropy of any compact group endomorphism. The goal of this paper is to prove a perfect analog of the Yuzvinski Formula for the algebraic entropy, namely, the Algebraic Yuzvinski Formula, giving the value of the algebraic entropy of an endomorphism of a finite-dimensional rational vector space as the Mahler measure of its characteristic polynomial.