Takens' Theorem: Proof and Applications

Abstract

[eng] In this work, we prove the Takens’ Embedding Theorem and we give a more general version of the Theorem. Firstly, we write a plotline to understand the theorem and the proofs. We follow mainly some articles, such as [1]. In some cases, we explain more the proofs and in others, we give some alternative proofs. We prove the Takens’ Embedding Theorem, as it appears in his article [2] and through it, we arrive at a more general result. This result appears in some references, but as far as we know, there is no explicit proof of this generalization. Finally, we make some applications to understand the use of the theorem. Some applications are theoretical, and others are practical. The theoretical experiments are given by dynamical systems and the practical are mainly from harmonic signals.