I am curious how to describe functions whose derivatives rapidly change sign (over a small domain). Oscillation is what comes to mind, however I am thinking of more general functions, which neither have regular periods, nor constant amplitudes.

My specific application is a mapping function between noisy inputs and outputs. If the noise is spread out over a local domain where the the function is smooth, and the derivative changes sign only once, then the map is easy to understand. However, if the noise is can produce values over a domain where the mapping function’s derivative changes sign multiple times within that range, then the mapping is highly multi-valued. I feel like this way of discussing it is cumbersome, and that there is a more succinct way to phrase this. Any help, or pointing to a good mathematical terminology reference resource would be much appreciated!

Thank you,

Brian

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