A note on positive Lyapunov exponent and sensitive dependence on initial conditions

Abstract In this note, we give two examples of discrete dynamics (functions) on intervals ⊂ R , the first having a positive Lyapunov exponent at a point but not being sensitive-dependent on initial conditions at that point; and the second being sensitive-dependent on initial conditions at a point but having a negative Lyapunov exponent at that point.