While I do not know what makes one country a dominant power, I know that if one country cannot impose its will on another, we have at least two poles. I do not believe that there was ever an "American world". There may have been an American "moment", and the moment --- in historic terms --- did not last long. I would say that the "moment" lasted between 1989 and 1999. It began with the fall of the Berlin Wall, and ended up in Kosovo. The fall of Berlin wall signified changes in Soviet Union that were irreversible. US and its allies had the world's attention. The US was faced with the decision on how to use that moment. One choice was world leadership, and another world domination. The US chose the other. Choosing a leadership role would have required moving UN as an organization towards major enhancement of the international law. There was nobody interested in challenging the US superpower status; the incentive for a more open, law obiding and peacefull world would have been acceptable. US needed to become a good manager, someone who does not play favorites, and someone who does not enrich himself at the expense of others. 1999, in a most blatant violation of international law, US and European allies crowned their dismemberment of Yugoslavia with the bombing campaign for no reason --- except to show that they could. Kosovo has always been a mystic land, and the curse seems to fall on those who rape it. In response, Shangai Cooperation Organization was founded, and Yeltzin gone from the scene. Nuclear might was resurected in Russia as a means of "convincing" others to give respect where due. And China, with Russia in its court, went on to change the world economy as we know it. As the bid for domination stalled, US is searching for answers. The new thinking keeps the world dominance as objective, but with promises to share some power. Remains to be seen.