Seminario

Seminario Geometría

Computability, noncomputability, and dynamical systems

Ponente:  Daniel S. Graça (Universidade do Algarve)
Fecha:  miércoles 19 de mayo de 2021 - 12:00
Lugar:  Online - zoom.us/j/2203382215

Resumen:
In this talk we will analyse several interconnections between computability and dynamical systems theory. In computability theory one is interested in knowing whether a problem is algorithmically solvable, where the notion of algorithm is made precise via an appropriate model of computation such as Turing machines. A remarkable insight from computability theory is that there are noncomputable problems which are algorithmically unsolvable, such as Hilbert`s 10th problem. In this talk we will survey two types of results. First we will study the computational power of some classes of smooth dynamical systems. Second, building on the previous results and on the framework of computable analysis when appropriate, we study the computability of some problems related to smooth dynamical systems (finding invariant sets, basins of attraction, etc.), showing that some of those problems are noncomputable.