Chaoslike behavior in nonchaotic systems at finite computation precision

The dynamical behavior of a two-dimensional map is investigated numerically. A chaoslike behavior, i.e., a nonsmooth distribution of the attractor and seemly sensitive dependence of the motion on initial condition is found as the system state is nonchaotic (both Lyapunov exponents are nonpositive). The key point for this strange behavior is that the mode corresponding to the second negative Lyapunov exponent contains positive local Lyapunov exponent segments. It is argued that this kind of behavior may be typical and easily observed in practical numerical computations and experiments where small noise is inevitable.