标题： 可计算动力系统中的普遍性：旧的和新的 显示英文标题

标题： Universality in computable dynamical systems: Old and new

摘要： 计算模型与动力学之间的关系自计算概念最早提出以来就吸引了数学家和计算机科学家。 最近，由于T. Tao的计划旨在通过嵌入式计算模型发现纳维-斯托克斯方程的爆破解，这一联系重新引起了关注。 在本综述论文中，我们回顾了一些最近的研究工作，这些工作为通过动力系统表示可计算性提供了新颖而令人兴奋的视角。 从经典意义上的动力学普遍性出发，我们将探讨流体动力学中的现代图灵普遍性和拓扑克莱因场理论，作为一种通过动力学 bordisms 系统表示可计算函数的方式。 最后，我们将讨论该领域的一些重要开放问题。 显示英文摘要

摘要： The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, this connection has gained renewed attention, fueled by T. Tao's programme aiming to discover blowing-up solutions of the Navier-Stokes equations using an embedded computational model. In this survey paper, we review some of the recent works that introduce novel and exciting perspectives on the representation of computability through dynamical systems. Starting from dynamical universality in a classical sense, we shall explore the modern notions of Turing universality in fluid dynamics and Topological Kleene Field Theories as a systematic way of representing computable functions by means of dynamical bordisms. Finally, we will discuss some important open problems in the area.