  Identifying behavior that is relatively invariant under different conditions
is a challenging task in far-from-equilibrium complex systems. As an example of
how the existence of a semi-invariant signature can be masked by the
heterogeneity in the properties of the components comprising such systems, we
consider the exchange rate dynamics in the international currency market. We
show that the exponents characterizing the heavy tails of fluctuation
distributions for different currencies systematically diverge from a putative
universal form associated with the median value (~2) of the exponents. We
relate the degree of deviation of a particular currency from such an "inverse
square law" to fundamental macroscopic properties of the corresponding economy,
viz., measures of per capita production output and diversity of export
products. We also show that in contrast to uncorrelated random walks exhibited
by the exchange rate dynamics for currencies belonging to developed economies,
those of the less developed economies show characteristics of sub-diffusive
processes which we relate to the anti-correlated nature of the corresponding
fluctuations. Approaches similar to that presented here may help in identifying
invariant features obscured by the heterogeneous nature of components in other
complex systems.
