Output digitization of simple measure-preserving linear systems
A.DeStefano1
M.Thitsa2
C.Martin3
1.Department of Mathematics and Computer Science,College of the Holy Cross,Worcester,MA 01610,USA2.Department of Electrical and Computer Engineering,Mercer University,Macon,GA 31207,USA3.Department of Mathematics and Statistics,Texas Tech University,Lubbock,TX 79430,USA
摘要：We examine three simple linear systems from the viewpoint of ergodic theory.We digitize the output and record only the sign of the output at integer times.We show that even with this minimal output we can recover important information about the systems.In particular,for a two-dimensional system viewed as a flow on the circle,we can determine the rate of rota-tion.We then use these results to determine the slope of the trajectories for constant irrational flow on the two-dimensional torus.To achieve this,we randomize the system by partitioning the state space and only recording which partition the state is in at each integer time.We show directly that these systems have entropy zero.Finally,we examine two four-dimensional systems and reduce them to the study of linear flows on the two-dimensional torus.
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论文发表日期：2021-11-05
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：14( 430-443 )
英文信息