The word gamaka is derived from the sam.skr.ta root gam - to go. The term daSa-gamaka is very familiar to most people. Nowadays, it is usual, especially among Carnatic music cirlces, to talk of gamaka as oscillation of the swara, or as ornamentation of the swara. It is also fashionable to say that Carnatic music is charaterized by the presence of gamakas and Hindustani music by the absence of them. I think this is a gross misrepresentation, arising out of a misunderstanding of the term gamaka.
Old sources refer to ten kinds of gamakas.
Examples are the ma in Sankarabharanam or the ga in Todi. The oscillation can start from a lower swara or a higher one. It may also center around the actual swarasthana, like the ri in Madhyamavati, in which case it is called andolana. However, the kampita gamaka is not an oscillation from a lower swara to a higher one without touching the actual swara itself. The enduring sound heard is the appropriate swara accompanied by the band of microtones allowed by the raga lakshana.