Abstract
We recently proposed a method for generating true orbits of one-dimensional piecewise linear fractional maps (Physica D, 268 (2014), 100-105). By applying the method to the continued fraction transformation and a modified Bernoulli map, we show that we can obtain true orbits which display the same properties as typical orbits of the two maps. We also conduct verification of Brillhart's cubic irrational that is known to display an unusual occurrence of large partial quotients in its continued fraction expansion, and we report that we can obtain results which support the safety of our true orbit generation method.
