Quasiperiodic function

Article summary

In mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. A function f is quasiperiodic with quasiperiod \omega if f(z + \omega) = g(z,f(z)) , where g is a "simpler" function than f . What it means to be "simpler" is vague. A simple case (sometimes called arithmetic quasiperiodic) is if the function obeys the equation f(z + \omega) = f(z) + C. Another case (sometimes called geometric quasiperiodic) is if the function obeys the equation f(z + \omega) = C f(z). An example of this is the Jacobi theta function, where \vartheta(z + \tau; \tau) = e^{-2\pi iz - \pi i\tau} \vartheta(z; \tau), shows that for fixed \tau it has quasiperiod \tau ; it also is periodic with period one. Another example is provided by the Weierstrass sigma function, which is quasiperiodic in two independent quasiperiods, the periods of the corresponding Weierstrass ℘ function. Bloch's theorem says that the eigenfunctions of a periodic Schrödinger equation (or other periodic linear equations) can be found in quasiperiodic form, and a related form of quasi-periodic solution for periodic linear differential equations is expressed by Floquet theory. Functions with an additive functional equation f(z + \omega) = f(z) + az + b are also called quasiperiodic.…

Key claims

No claims recorded.

Discussion questions

1. Summarise the article in your own words. Which single claim would you verify first, and why?
2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

No sources recorded.