Seminar on Applied Mathematics: Takens’ Embedding Theorem

Speaker: Jordi Penalva Vadell

Title: Takens’ Embedding Theorem

Abstract:

Takens’ Embedding Theorem is a very extended result into time-series analyses and it is commonly used into a lot of branches, such as psychology or economies, where it is natural the usage of time-series. It allows to recover the attractor from the dynamical system. From the attractor, we can find some basic properties from the system, such as the dimension or the fractal dimension.

In this talk, I will explain the meaning of the Theorem, next I will give a sketch of the proof and finally we will see how to obtain the dynamical system from the signals. We will use some classic examples: the circumference, the torus and the Lorenz system.