We present an efficient method for fast, complete, and accurate detection ofunstable periodic orbits in chaotic systems. Our method consists of a newiterative scheme and an effective technique for selecting initial points. Theiterative scheme is based on the semi-implicit Euler method, which has bothfast and global convergence, and only a small number of initial points issufficient to detect all unstable periodic orbits of a given period. The powerof our method is illustrated by numerical examples of both two- andfour-dimensional maps.
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