An Efficient Method for Computing Periodic Orbits of Conservative Dynamical Systems
The accurate computation of periodic orbits and the precise knowledge of their properties are very important for studying the behavior of many dynamical systems of physical interest. In this paper, we present an efficient numerical method for computing to any desired accuracy periodic orbits (stable, unstable and complex) of any period. This method always converges rapidly to a periodic orbit independently of the initial guess, which is important when the mapping has many periodic orbits, stable and unstable close to each other, as is the case with conservative systems. We illustrate this method first, on the 2-Dimensional quadratic Hénon’s mapping, by computing rapidly and accurately several periodic orbits of high period. We also apply our method here to a 3-D conservative mapping as well as a 4-D complex version of Hénon’s map.
KeywordsPeriodic Orbit Rotation Number Topological Degree Bisection Method Unstable Periodic Orbit
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