动力学次数、算术次数与规范高度：历史、猜想与未来方向
数论
2024-08-06 v1 动力系统
摘要
本文概述了用于衡量代数动力系统 复杂度的各种量，包括给出代数函数迭代几何复杂度的保守度 ，给出代数点 在 中轨道算术复杂度的保守度 ，以及各种版本的规范高度 ，这些提供了更精细的算术复杂度度量。文中重点关注开放问题及进一步探索的方向。
引用
@article{arxiv.2408.01559,
title = {Dynamical Degrees, Arithmetic Degrees, and Canonical Heights: History, Conjectures, and Future Directions},
author = {Joseph H. Silverman},
journal= {arXiv preprint arXiv:2408.01559},
year = {2024}
}
备注
To appear in the proceedings of the Simons Symposia on Algebraic, Complex, and Arithmetic Dynamics. This article is an expanded version of a talk presented at the Simons Symposium, May 2019, Germany. A small number of updates were added in 2023 and 2024 and are noted as such. 19 pages