There are no actual deserts in Cyprus as there are in the Middle East- the nearest you get to such a thing are large areas of rough white stony ground dotted with scrubby bushes, stunted olive and fir trees, and thickets of brambles. However, none of these are large enough to have names of their own- they are usually bordered by farmland or by housing development, Cyprus being a small country and needing to make maximum use of it's land area.
Greece has no deserts.
no there was not a desert in ancient greece.
No there aren't.
Haiti has no deserts.
There are no deserts in Delaware.
Japan has no deserts.
There are no deserts in Rome.
Honduras has no deserts.
Greece has mountains, is not in the tropics and has no deserts.
Alaska has no true deserts.
Alabama has no true deserts.
There are no deserts in Ireland.