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The chaotic behavior of uniformly hyperbolic systems is well known. Geodesic flows with negative Gaussian
curvature are among the well characterized examples of such systems, as it is proved that a geodesic flow on
a compact factor of the hyperbolic plane is an Anosov flow. However, surfaces with constant negative Gaussian curvature cannot be realized as an embedded surfaces in R^3 and hence were thought to be physically unrealizable until recently. On the other hand, it is known that every compact orientable surface of negative Euler characteristics, i.e. with genus more than one, supports a Riemannian metric of constant negative Gaussian curvature and it has been recently proved that for any compact orientable closed surface of genus greater or equal to zero, there exists a mechanical linkage, such that its configuration space is homeomorphic to the surface. To this end, another recent
study identified a detailed numerical example of a triple mechanical linkage with a uniformly chaotic attractor.
In this paper, this topic of physical realization of uniformly chaotic behavior is studied, understood and reviewed with necessary background materials. |
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