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hyperbolic critical point A critical point hyperbolic equation A second-order par-
m of a vector field X (i.e., X(m ) = 0) is called tial differential equation of the form
0
0
hyperbolic or elementary if none of the eigenval-
ues of the linearization X (m ) (called character- Au + Bu + Cu + Du + Eu + Fu = G

0 xx xy yy x y
istic exponents) has zero real part. Liapunov’s
2
theorem shows that near a hyperbolic critical such that B − 4AC > 0. It is called parabolic
2
2
point the flow looks like that of its linearization. if B − 4AC = 0 and elliptic B − 4AC < 0.

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