Critical Points of Nonlinear Systems

There is an error in Boyce/diPrima in table 9.3.1 on page 484 about types of critical points of almost linear systems:

r₁ = r₂ > 0 or r₁ = r₂ < 0

the type of the almost linear system should be more general types of N, SpP (which can look different from the nodes and spiral points for linear systems) . In this case the statement below the table (that the slopes are the same as for the linear equation) is not always true.

r₁ = i , r₂ = -i with nonzero

the type of the almost linear system should be C, SpP or other.

In these cases even very near the critical point the trajectories of the nonlinear system can be very different from those of the linear system.

Here is a correct table. One can construct examples where ``other'' types than the ones in table 9.3.1 occur.