Universality in computable dynamical systems: old and new
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, fuelled by T. Tao’s programme aiming to discover blowing-up solutions of the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/446068 |
| Acceso en línea: | https://hdl.handle.net/2117/446068 https://dx.doi.org/10.1088/2632-072X/ae00b5 |
| Access Level: | acceso abierto |
| Palabra clave: | Turing machine Universality Fluid computers Euler equations Reeb vector fields Beltrami vector fields Contact geometry Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | 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, fuelled 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. |
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