The expression gestural mapping is well imbedded in the language of instrument designers, describing the function from interface control parameters to synthesis control parameters. This function is in most cases implicitly assumed to be instantaneous, so that at any time its output depends only on its input at that time. Here more general functions are considered, in which the output depends on the history of input, especially functions that behave like physical dynamic systems, such as a damped resonator. Acoustic instruments are rich in dynamical behaviour. Introducing dynamics at the control stage of an electronic instrument can help compensate for lack of dynamics in later non-physical synthesis stages. A broadening of the function space offers new aesthetic possibilities for composing instruments. Examples are presented to illustrate the new design/composition mode as well as practical techniques. In this context, it is suggested that the word mapping be updated with the more descriptive expression dynamic control processing.