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Discretization of Homoclinic Orbits, Rapid Forcing and ``Invisible'' Chaos
Bernold FiedlerJürgen Scheurle
出版American Mathematical Soc., 1996
主題Mathematics / Algebra / GeneralMathematics / CalculusMathematics / Differential Equations / GeneralScience / Chaotic Behavior in Systems
ISBN08218046859780821804681
URLhttp://books.google.com.hk/books?id=H3bTCQAAQBAJ&hl=&source=gbs_api
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註釋Numerically speaking, continuous time dynamical systems do not exist. Rather, a discretized version is studied and interpreted in analogy to the continuous time dynamical system. Over fixed finite time intervals, this analogy is quite close and well understood in terms of discretization errors and sophisticated discretization schemes. Over large or infinite time intervals, this analogy is not so clear, because discretization errors tend to accumulate exponentially with time. In this paper, we specifically investigate the correspondence between continuous and discrete time dynamical systems for homoclinic orbits. By definition, these are orbits which tend to the same stationary point for both large positive and large negative times.