regarding who is owner/ruler of the world:
The earth is the LORD's, and all its fullness, the world and those who dwell therein. Psalm 24:1
. . . you may know that the earth is the LORD's.
Exodus 9:29
. . . for all the earth is Mine.
Exodus 19:5
The heavens are Yours, the earth also is Yours; the world and all its fullness, You have founded them. Psalm 89:11
Satan is ruler of the fallen world system, not the world.
I can't find one single scripture that states that Satan is ruler/authority over the world. I can't even find one that says Satan has the power to establish any kingdom.
in Genesis, MAN is given dominion over the world.
"The highest heavens belong to the LORD, but the earth he has given to man." Psalm 115:16
It seems that during the temptation of Jesus that either Satan isn't sure He is the son of God, or he is testing Jesus' faith in the matter. "If you are the Son of God..."
There is some thought on the idea that the dominion of the world (while the world/earth/heavens are owned by God) rests in whomever claims it.
Quoting: Salt
Why Did Jesus Choose Neutrality?Jesus’ neutrality regarding the politics of this world was well-grounded in Scriptural principles. Consider just two.
“Man has dominated man to his injury.” (Ecclesiastes 8:9) That is how the Bible sums up the history of human rule. Remember, Jesus existed as a spirit in heaven long before he came to earth as a man. (John 17:5" So now you, Father, glorify me alongside yourself with the glory that I had alongside you before the world was".) He thus knew that man, however well-meaning, lacks the ability to care properly for the needs of billions of people; nor was he created by God to do so. (Jeremiah 10:23" I well know, O Jehovah, that to earthling man his way does not belong. It does not belong to man who is walking even to direct his step.") Jesus knew that the solution to mankind’s problems lay elsewhere—not in human governments.
“The whole world is lying in the power of the wicked one.” (1 John 5:19) Do you find that statement startling? Many do. They think of sincere people who get involved in government because they want to make the world a better, safer place. Try as they might, though, even the most sincere rulers cannot overcome the influence of the one whom Jesus called “the ruler of this world.” (John 12:31" Now there is a judging of this world; now the ruler of this world will be cast out"; 14:30" I shall not speak much with YOU anymore, for the ruler of the world is coming. And he has no hold on me, ") That is why Jesus said to one worldly politician: “My kingdom is no part of this world.” (John 18:36) Jesus was the prospective King of God’s heavenly government. Had Jesus mixed in politics, he would have sacrificed his loyalty to his Father’s government.
Did Jesus teach, then, that his followers have no obligation to earthly governments? On the contrary, he taught them how to find the right balance between their responsibilities toward God and their obligations toward secular governments.