Provide a complete description of the conjugacy classes for

Provide a complete description of the conjugacy classes for 2 times 2 systems in the nonhyperbolic case.

Solution

In nonhyperbolic case, two matrices form conjugacy classes for 2 x 2 system if both sets of eiganvalues do not fall in the same category i.e.

(i) If one eigan value is negative then second will not be positive.

(ii) Both eigan values do not have negative real parts.

(iii) Both eigan values do not have positive real parts.