An important problem in physics is the study of the transport for locally conserved quantities. One typical example is a gas of interacting particles. This problem can be very difficult, hence to study it a possibility is simplify the system, preserving its deterministic nature. An efficient model for this problem is the so called "deterministic walk". In this talk I consider the case in wich the local dynamics is the simplest possible and yet retains the characteristic of being chaotic, that is it displays a strong dependence from initial conditions: a piecewise smooth expanding map. In particular I discuss the limit behaviour and a mixing property of this model.

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