Maps with precision-dependent periods

Abstract

There exists a class of maps that possesses nonchaotic orbits with either finite or infinite periods. However, these maps have computationally determined periods that are dependent on the precision of the arithmetic. Such maps are said to have relative, apparently real periods.$- We give analytical proof that a special case of the logistic map with a discontinuity belongs to this class and support this proof with some numerical illustrations. © 1991 The American Physical Society.