On the numerical computation of orbits of dynamical systems: The higher dimensional case

✍ Scribed by Shui-Nee Chow; Kenneth J Palmer

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 969 KB
• Volume: 8
• Category: Article
• ISSN: 0885-064X
• DOI: 10.1016/0885-064x(92)90004-u

✦ Synopsis

Chaotic dynamical systems exhibit sensitive dependence to initial conditions. So, because of round-off error, a computed orbit diverges at an exponential rate from the true orbit with the same initial condition. Nevertheless, we are able to exploit the hyperbolicity of the dynamical system to prove a "finite time" shadowing lemma, from which we deduce that a true orbit shadows the computed orbit for a large number of iterates. An algorithm for the computation of the shadowing error is given and, furthermore, the effect of round-off error on these computations is analyzed in detail. The algorithm is applied to the Htnon map. This paper is a continuation of an earlier paper on one-dimensional maps.