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Share  Title: Physical Realization of Chaotic Behavior: A Review

 

 
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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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Keywords

Uniformly  Chaotic  Behavior,  Anosov  Flows,  Mechanical  
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 About This Document
 
 Subject Mathematics
 Category MS Thesis
 Views 3084
 Downloads 215
 Added 25-11-09
 Contributor   soumikpsu
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