Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.10725 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908509255237632 |
|---|---|
| author | González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel |
| author_facet | González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality in computable dynamical systems: Old and new González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel Dynamical Systems Formal Languages and Automata Theory Differential Geometry 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. |
| title | Universality in computable dynamical systems: Old and new |
| topic | Dynamical Systems Formal Languages and Automata Theory Differential Geometry |
| url | https://arxiv.org/abs/2507.10725 |