Is it possible to use a Volterra series to generate subharmonics? Taylor series can create harmonics of the frequencies in an input signal. I'm wondering if it is likewise possible to use Volterra series to create sub-harmonics of the frequencies in that signal.

Some degree of finesse is required in posing the question:

Taylor series don't only create harmonics; there's intermodulation distortion as well. Likewise, it's ok with me if a suitable Volterra series doesn't only create sub-harmonics, but also creates something similar to intermodulation distortion, or even some degree of harmonic distortion.

However, I would like to exclude trivial cases where the input signal gets so wrecked that it ends up looking like white noise, which would obviously create sub-harmonics (along with every other frequency you can imagine!). I'm not sure how to formalize this requirement precisely, other than to say that I hope it's clear what I'm driving at.

Here's one way to formalize the behaviour I want:


Given an input $\cos(\omega t)$, yields an output containing $\cos(\frac{\omega}{n} t)$ for 
some fixed $n$, ideally a natural number
Given a general input, a sub-harmonic is generated corresponding to every frequency in the input
Other "intermodulation distortion"-type artifacts are allowed, "within reason"


The answer can be expressed for either discrete or continuous signals.
Check out this paper.  I would have made a comment but not high enough rep.  

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&amp;arnumber=1211087&amp;url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F81%2F27258%2F01211087

Looks like you need multiple in to get subharmonics in Volterra series

The abstract states "Subharmonic generation is a complex nonlinear phenomenon which can arise from nonlinear oscillations, bifurcation and chaos. It is well known that single-input-single-output Volterra series cannot currently be applied to model systems which exhibit subharmonics. A new modeling alternative is introduced in this paper which overcomes these restrictions by using local multiple input single output Volterra models. The generalized frequency-response functions can then be applied to interpret systems with subharmonics in the frequency domain."