Dynamics and entropy in local algebra
Algebraic Geometry
2011-09-30 v1 Commutative Algebra
Dynamical Systems
Abstract
We introduce and study a notion of algebraic entropy for self-maps of finite length of Noetherian local rings, and develop its properties. We show that it shares the standard properties of topological entropy. For finite self-maps we explore the connection between the degree of the map and its algebraic entropy, when the ring is a Cohen-Macaulay domain. As an application of algebraic entropy, we give a characteristic-free interpretation of the definition of Hilbert-Kunz multiplicity.
Cite
@article{arxiv.1109.6438,
title = {Dynamics and entropy in local algebra},
author = {Mahdi Majidi-Zolbanin and Nikita Miasnikov and Lucien Szpiro},
journal= {arXiv preprint arXiv:1109.6438},
year = {2011}
}
Comments
20 pages