A hyperbolic fixed point of an autonomous differential equation is a fixed point for which every eigenvalue
of the stability matrix has a nonzero real part. In two dimensions, eigenvalues 
give the special
case of a saddle point. Eigenvalues
with real parts all of the same sign instead give a
hyperbolic sink or source.
In the classification of nonidentity linear fractional transformations 
with real
coefficients and 
, the hyperbolic case is characterized
by
See also
Elliptic Fixed Point,
Fixed Point,
Linear
Transformation,
Parabolic Fixed Point,
Stable Improper Node,
Stable
Spiral Point,
Stable Star,
Unstable
Improper Node,
Unstable Node,
Unstable
Spiral Point,
Unstable Star
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References
Tabor, M. "Classification of Fixed Points." §1.4.b in Chaos
and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley,
pp. 22-25, 1989.Referenced on Wolfram|Alpha
Hyperbolic Fixed Point
Cite this as:
Weisstein, Eric W. "Hyperbolic Fixed Point."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HyperbolicFixedPoint.html
Subject classifications
