arXiv subjects

Georg Ostrovski

Publications and source records attributed to Georg Ostrovski.

21 records · Page 2Linked to original sources

arXiv2013

Dynamics of a Continuous Piecewise Affine Map of the Square

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 coexistence of stochastic and (quasi-)periodic behaviour, we investigate invariant annuli separated by invariant circles. For certain parameter values, we explicitly construct invariant circles both of rational and irrational rotation numbers, and present numerical experiments of the dynamics on the annuli bounded by these circles.

math.DS↗

arXiv2013

Fixed Point Theorem for Non-Self Maps of Regions in the Plane

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 translation theorem for self-maps of the plane, we prove that f has no recurrent (in particular, no periodic) points if it has no fixed points.

math.DS↗

arXiv2010

Piecewise Linear Hamiltonian Flows Associated to Zero-Sum Games: Transition Combinatorics and Questions on Ergodicity

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.

math.DS↗