This territorial dispute between Japan and South Korea over Takeshima(Dokdo) is quite simple.
1. There is no historical fact that Korea had ever exercised any "effective control" over the islets prior to 1905.
2. Japan officially incorporated the islets in 1905 strictly following the procedures prescribed in the International law.
3. After the WW2, the Allies determined that Takeshima/Dokdo should remain Japanese territory in the San Francisco Peace Treaty in 1951.
4. Though the South Korean government had been informed of the determination by the U.S. government in those diplomatic documents like "Rusk documents", they ignored this international determination and started occupying the islets illegally from 1952.