Convergence analysis of Davidchack and Lai’s algorithm for finding periodic orbits. (English) Zbl 1024.37020
For an algorithm finding not necessarily stable periodic points of discrete dynamical systems in Euclidean space – developed by Davidchack and Lai – the authors give a rigorous proof of convergence and prove at least quadratic convergence. The algorithm is a modified Newton method which constitutes an almost implicit Euler method for a related differential equation, and contains sufficient parameters for adjustment to be applied to special cases in a flexible way, e.g. stabilizing the target points. A discussion of examples is included.
Reviewer: Dieter Erle (Dortmund)
MSC:
| 37D05 | Dynamical systems with hyperbolic orbits and sets |
| 37C27 | Periodic orbits of vector fields and flows |
| 65P40 | Numerical nonlinear stabilities in dynamical systems |
Keywords:
hyperbolic periodic orbits; numerical algorithm; basin of attraction; Newton method; switching matrixSoftware:
DynamicsReferences:
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