Dominance requires sound economics - and this is what will determine the future course of history. Lookout for China, it is not falling aprt - but will be the economic superpower of the world by 2018. And beware of India, which will relegate the US to third spot by 2030. And let us talk then!
The law of big numbers is harder to climb than the projectors would ever like to admit. Which is why the Japanese and German 'miracle' economies of the mid 1960s-1980s didn't lead to either of them becoming super powers.
China and India will have a much harder road than most are willing to admit. India is already displaying massive political paralysis, with an economy that has stopped growing properly. China is taking on very large amounts of debt domestically, with national growth that has slowed considerably (and some would say dramatically, as numbers are being lied about at a local level to falsify growth according to a recent NY Times article). If you run what may in fact be 4% to 5% national growth against their inflation rate, the Chinese economy has all but stopped growing (which explains the massive sitting hoards of commodities at their distribution points that are going unused and the collapse in electricity usage). China had to instigate a huge real estate bubble to keep their economy going, using substantial stimulus to generate 'growth.' As those imbalances in their economy adjust, growth will be harder and harder to come by. Studies have shown that for each dollar of investment that China makes, they're getting radically less growth out of it than they were 10 or 15 years ago.