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math.DS2013★ 1 cited
Dynamics of a Continuous Piecewise Affine Map of the Square
Georg Ostrovski
We present a one-parameter family of continuous, piecewise affine, area preserving maps of the square, which are inspired by a dynamical system in game theory. Interested in the co…
math.DS2011★ 2 cited
Fixed Point Theorem for Non-Self Maps of Regions in the Plane
Georg Ostrovski
Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane tra…
math.DS2010★ 5 cited
Piecewise Linear Hamiltonian Flows Associated to Zero-Sum Games: Transition Combinatorics and Questions on Ergodicity
Georg Ostrovski, Sebastian van Strien
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…