I am looking for any recent studies dealing substantially with "broken vowels," or vocoid elements which have a noticeably nonstable formant trajectory, yet for which there are no good phonological arguments that they are diphthongs. "Broken vowels" might alternately be referred to as vowels with an "offglide" or "onglide".
To give an example, in the dialect of Vietnamese spoken around Cần Thơ, open syllables whose vowel is represented by an orthographic i or y are pronounced approximately with a vowel sounding like [ɨi], so mì 'wheat noodles' is pronounced approximately [mɨi]. Orthographic o, on the other hand, is pronounced more or less like [ɑ], so mỏ 'snout' is pronounced [mɑ]. It is difficult to argue that [ɨi] is really a combination of [ɨ] and [i], because there are no open-syllable words having nuclear vowel [ɨ], and none having [i]; there is also no difference in vowel length between mì and mỏ. Anyways, let's try not to quibble over the this specific example more than necessary...