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Microdynamics for Nash maps

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  • We investigate a family of maps that arises from a model in economics and game theory. It has some features similar to renormalization and some similar to intermittency. In a one-parameter family of maps in dimension 2, when the parameter goes to 0, the maps converge to the identity. Nevertheless, after a linear rescaling of both space and time, we get maps with attracting invariant closed curves. As the parameter goes to 0, those curves converge in a strong sense to a certain circle. We call those phenomena microdynamics. The model can be also understood as a family of discrete time approximations to a Brown-von Neumann differential equation.
    Mathematics Subject Classification: 37C70, 37E30.


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