I'm looking at the Arpabet page on Wikipedia, and note some entries like this:
Arpabet | IPA | Word Examples ER | ɝ | her (HH ER0); bird (B ER1 D); hurt (HH ER1 T), nurse (N ER1 S)
Now, I'm trying to convert this Arpabet "ER" into X-SAMPA. But, I don't see ɝ anywhere in the X-SAMPA specification. Instead, my reading leads me to see that character ɝ (and some others, like ɚ) are "R-colored vowels", which I think means they can be decomposed into two separate characters instead of written in one digraph character.
My question, in short, is: are these equivalent?
ɝ => ɜr ɚ => ər ɑ˞ => ɑr ɔ˞ => ɔr