how The US compares in mobility to other countries
http://www.epi.org/publication/usa-lags-peer-countries-mobility/
In truth, those correlations for father-son income are somewhat low in absolute terms, even if higher than most other countries. A .47 correlation means that only 22% of the variance in son's income is predicted by father's income, meaning that 78% of the variance is not predicted. However, such correlations are a really poor under-estimate of the true dependence of income on parental income. Changes in relative income inequality from generation to generation will lower the correlation, even if the change is increased inequality and it reflects a rich get even richer effect from father to son. IOW, if a person born into poverty stays poor but a person born into wealth is able to use that wealth to get even wealthier than their parents (which is what every scientific model of recent economic changes in the US shows is happening), this will reduce the inter-generational correlation. IOW, the dependence of wealth on parental wealth is very strong but it is non-linear because the more wealth you start with the more ability you have to increase your wealth beyond the wealth you were born into. This non-linear feature of the relationship weakens the observed simple linear correlation such as used in the cited "elasticity" index.
Such calculations should be done on income percentile, not dollars per se. That would eliminate what you are talking about.