Abstract
The accurate computation of periodic orbits and the knowledge of their stability properties are very important for studying the behavior of many physically interesting dynamical systems. In this paper, we describe first an efficient numerical method for computing periodic orbits of 4D mappings of any period and to any desired accuracy. This method always converges rapidly to a periodic orbit independently of the initial guess, which is very useful when the mapping has many periodic orbits close to each other, as in the case of conservative maps. We illustrate this method on a 4D symplectic mapping, by computing some of its periodic orbits and determining their particular arrangement in the 4D space, according to their stability characteristics. We then obtain periodic orbits associated with sequences of (rational) winding numbers converging on a pair of irrationals and discuss the possible existence of an analogue of Greene’s criterion for 4D symplectic mappings.
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