  This work's purpose is to understand the dynamics of limit order books in
order-driven markets. We try to illustrate a dynamical trading mechanism
attached to the microstructure of limit order markets. We capture the iterative
nature of trading processes, which is critical in the dynamics of bid-ask pairs
and the switching laws between different traders' types and their orders. In
general, after introducing the atomic trading scheme, we study a general
iterated trading process in both combinatorial and stochastic ways, and state a
few results on the stability of a dynamical trading system. We also study the
controlled dynamics of the spread and the mid-price in an iterated trading
system, when their movements, generated from the dynamics of bid-ask pairs, are
assumed to be restricted within some extremely small ranges.
