Luk 21:20 And when ye shall see Jerusalem compassed with armies, then know that the desolation thereof is nigh.
They are called the "abomination of desolation" in the parallel passages because they were heathens and idolaters, also carrying the images of their gods upon their standards as they marched to destroy Jerusalem.
Jerusalem is the city where the people of God reside, i.e. the Church.
the only “holy place” after Jesus went to the cross is the Church.
Jesus is warning that near the end of the world, Satan will be loosed for a short while, evil will multiple, there will be a great falling away from the Church such that Jesus asked whether He would still find faith on the earth when He returned and finally Satan will sit in the holy place, that is he will rule the Church. everything is playing out exactly as the Scriptures tell us they will.