Let X = X(t) be the solution of the plane autonomous system x' = Y y' = -x - (1 - i2 )y
Chapter 11, Problem 19(choose chapter or problem)
Let X = X(t) be the solution of the plane autonomous system x' = Y y' = -x - (1 - i2 )y that satisfies X(O) = (x0, y0) . Show that ifx5 + y5 < 1, then lim1--->ooX(t) = (0, 0). [Hint: Select r < 1 withx5 + y5 < r2 and first show that the circular region R defined by x2 + y2 ::5 r2 is an invariant region.]
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