Piecewise linear Hamiltonian flows associated to zero-sum games: transition combinatorics and questions on ergodicity

2011, Volume 16, Numbers 1-2, pp. 128-153

Author(s): Ostrovski G., van Strien S.

In this paper we consider a class of piecewise affine Hamiltonian vector fields whose orbits are piecewise straight lines. We give a first classification result of such systems and show that the orbit-structure of the flow of such a differential equation is surprisingly rich.

Keywords: Hamiltonian systems, non-smooth dynamics, Filippov systems, piecewise affine, Arnol’d diffusion, fictitious play, best-response dynamics, learning process

Citation: Ostrovski G., van Strien S., Piecewise linear Hamiltonian flows associated to zero-sum games: transition combinatorics and questions on ergodicity, Regular and Chaotic Dynamics, 2011, Volume 16, Numbers 1-2, pp. 128-153

DOI: 10.1134/S1560354711010059

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