  In many applications, there is a desire to determine if the dynamics of
interest are chaotic or not. Since positive Lyapunov exponents are a signature
for chaos, they are often used to determine this. Reliable estimates of
Lyapunov exponents should demonstrate evidence of convergence; but literature
abounds in which this evidence lacks. This paper presents two maps through
which it highlights the importance of providing evidence of convergence of
Lyapunov exponent estimates. The results suggest cautious conclusions when
confronted with real data. Moreover, the maps are interesting in their own
right.
