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Hyperbolic Fixed Point


A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point.

A hyperbolic fixed point of a map is a fixed point for which the rescaled variables satisfy

 (delta-alpha)^2+4betagamma>0.

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 Web Resource. https://mathworld.wolfram.com/HyperbolicFixedPoint.html

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