Very generally spoken, the "Greeks" we know from the classical times were not a single people. With the decline of the Mycenean civilization, or after it, indo-european groups which were probably very related to each other came into Greece bit by bit. Very probably it was not a real "invasion" nor a replacement of the old populace. The "Aegean substrate" (pre-indoeuropean peoples) existed almost everywhere, especially in Arkadia. The helotes and partially the perioics of the Spartans would be very much people of non-european descendance. From the "newcomers", the Dorians were one of the strongest groups, especially on the Peloponnes and central Greece. The Ionians (who include the Athenians) were another indoeuropean group but possibly merged more with the "conquered" population. In the end, the Indoeuropeans and the "Aegean substrate" could not be distinguished anymore, what remained were certain differences in the dialects, but that also applied between the Indoeuropean groups themselves...