I only think that their "dominance" has decreased as our definition of dominance has changed. We no longer see dominance as purely military, our idea of dominance is now largely based around economic factors.
The US will have the greatest military force well into the future. The US has also always had economic competitors. There have been no times in history where the US has had economic superiorty. They've always been competing with strong economies in Europe and Asia. If you compare the GDP of the US to the GDP of Germany of Japan over the last 50 years very little has changed.
Currently the US is having financial difficulties, but this isn't something new. In the 1970s there was major inflation. The 1980/1990s had their fair share of bad times and debt rose substantially.
http://en.wikipedia.org/wiki/File:US...since_1980.jpg
The US's overall share of GDP is slightly down. But this has more to do with an expanding and more affluent global population than a downward and sustained trend in the US economy. The overall change in % of PPP is also very low. Not enough to declare some kind of defeat of an empire, well if there ever was one.