  Economy is demanding new models, able to understand and predict the evolution
of markets. To this respect, Econophysics offers models of markets as complex
systems, that try to comprehend macro-, system-wide states of the economy from
the interaction of many agents at micro-level. One of these models is the
gas-like model for trading markets. This tries to predict money distributions
in closed economies and quite simply, obtains the ones observed in real
economies. However, it reveals technical hitches to explain the power law
distribution, observed in individuals with high incomes. In this work, non
linear dynamics is introduced in the gas-like model in way that an effort to
overcome these flaws. A particular chaotic dynamics is used to break the
pairing symmetry of agents $(i,j)\Leftrightarrow(j,i)$. The results demonstrate
that a "chaotic gas-like model" can reproduce the Exponential and Power law
distributions observed in real economies. Moreover, it controls the transition
between them. This may give some insight of the micro-level causes that
originate unfair distributions of money in a global society. Ultimately, the
chaotic model makes obvious the inherent instability of asymmetric scenarios,
where sinks of wealth appear and doom the market to extreme inequality.
