同宿点、非环多项式与代数Z^d作用的周期点
动力系统
2015-12-23 v2 代数几何
摘要
循环代数Z^d作用由d个交换变量中的Laurent多项式理想定义。当且仅当该理想的复簇与乘法d环面不相交时，此类作用是扩张的。对于此类扩张作用，已知周期点增长率的极限存在且等于该作用的熵。在早先的论文中，作者将此结果推广到了簇与d环面相交为有限集的理想。在此，我们进一步将其推广到簇与d环面相交的维度至多为d-2的情形。主要工具是构造衰减足够快以致可求和的同宿点。
引用
@article{arxiv.1108.4989,
title = {Homoclinic points, atoral polynomials, and periodic points of algebraic Z^d-actions},
author = {Douglas Lind and Klaus Schmidt and Evgeny Verbitskiy},
journal= {arXiv preprint arXiv:1108.4989},
year = {2015}
}
备注
23 pages, corrected an error in the calculation of periodic components, but this does not affect the results. Accepted for publication by Ergodic Theory & Dynamical Systems