Abstract
An intensively used method for finding periodic orbits is Newton’s method and variants thereof. We describe Newton’s method and the Quasi-Newton method later in this section. Newton→s method uses the initialization point y1, marked by the small cross, as its initial point. These methods converge to a periodic point with the desired period if the initial condition is reasonably close to it, provided +1 is not an eigenvalue of the Jacobian matrix of the nth iterate of the process, where n is the period (see below).
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References related to Dynamics
J.H. Verner, Explicit Runge-Kutta methods with estimates of the local truncation error, SIAM J. Numer. Anal. 15 (1978), 772–790
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© 1994 Springer-Verlag New York, Inc.
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Nusse, H.E., Yorke, J.A., Kostelich, E.J. (1994). Finding Periodic Orbits. In: Dynamics: Numerical Explorations. Applied Mathematical Sciences, vol 101. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0231-5_10
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DOI: https://doi.org/10.1007/978-1-4684-0231-5_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94334-3
Online ISBN: 978-1-4684-0231-5
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