We study a model of piecewise rational rotations of a triangle for which the aperiodic
orbits generate complex geometric structure without exponential divergence of nearby orbits.
Such behavior, known as pseudochaos,is similar to that of sticky orbits of chaotic Hamiltonian
systems in the presence of self-similar island-around-island configurations in phase space.
In our piecewise rotation model, the triangle admits a recursive sequence of tilings which
makes possible the proof of a number of exact theorems and the extraction of high-precision
numerical results. We derive a hierarchical symbolic dynamics for the aperiodic orbits, and
calculate numerically the spectrum (q) of generalized dimensions for recurrence times. The
values (0) and (1) are Hausdor dimensions which can obtained as solutions of relatively
simple transcendental equations. The value q0 such that (q0) = 0 gives the exponent of the
power-law growth in the number of periodic orbits as a function of period. Finally, we study
the one-dimensional walk obtained by using the map on a triangle to generate an aperiodic
sequence of pseudo-random numbers.
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