hamartia is displayed when Oedipus swears to horribly punish Laius' killer right when he finds out without knowing that it's actually him
"Now my curse on the murderer. Whoever he is... let that man drag out his life in agony, step by painful step-" (280-284)
"I brought down these piling curses on myself!... I've touched your body with these, the hands that killed your husband" (906-909)
peripeteia is shown when Oedipus discovers that he is the true murderer of Laius
"the child came from the house... of Laius...they said it was-his son!" (1282-1287)
anagorisis is presented when Oedipus realizes his true birth when the Shepard tells him how he isn't the real son of Polybus & Merope and is actually the son of Laius & Jocasta
Oedipus immediately cursed the killer and assumed it wasn't him, which was his error in judgement. The fact that he's the killer will lead to his downfall.
Peripeteia, or a sudden reversal in circumstances. Oedipus spends all this time hating and trying to find out who the killer is but it just ends up being him the entire time.
Oedipus realizes his true identity as the son of Laius and Jocasta because of the Shepard's story, which proved the prophecy true. Which is ironic because he came to Thebes trying to get away from Polybus to prevent the prophecy because he believed that he was his real father.