Discretization of Homoclinic Orbits, Rapid Forcing and ``Invisible'' Chaos
Bernold Fiedler · Jürgen Scheurle
Jan 1996 · American Mathematical Society: Memoirs of the American Mathematical Society Book 570 · American Mathematical Soc.
Ebook
79
Pages
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About this ebook
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.
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