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Quasiperiodic function 📂Functions

Quasiperiodic function

Definition 1

A function $h : \mathbb{R} \to \mathbb{R}^{n}$ is said to be quasiperiodic if it can be expressed in terms of a basic frequency $\omega_{1} , \cdots , \omega_{n}$ and for each $x_{1} , \cdots , x_{n}$ there exists a $2 \pi$-periodic function $H$ such that the following holds $h$. $$ h(t) = H \left( \omega_{1} t , \cdots , \omega_{n} t \right) $$

Explanation

A quasiperiodic function is not literally a periodic function, but it possesses similar properties. For instance, the $h$ defined as follows is a quasiperiodic function. $$ h(t) = r_{1} \cos \omega_{1} t + r_{2} \sin \omega_{2} t $$

On the other hand, a quasiperiodic function with infinitely many basic frequencies may also be referred to as an almost periodic function.


  1. Wiggins. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos Second Edition(2nd Edition): p803. ↩︎