In the study of dynamical systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds. Near a hyperbolic point the orbits of a two-dimensional, non-dissipative system resemble hyperbolas. This fails to hold in general. Strogatz notes that "hyperbolic is an unfortunate name—it sounds like it should mean 'saddle point'—but it has become standard."[1] Several properties hold about a neighborhood of a hyperbolic point, notably[2]
- A stable manifold and an unstable manifold exist,
- Shadowing occurs,
- The dynamics on the invariant set can be represented via symbolic dynamics,
- A natural measure can be defined,
- The system is structurally stable.
- ^ Strogatz, Steven (2001). Nonlinear Dynamics and Chaos. Westview Press. ISBN 0-7382-0453-6.
- ^ Ott, Edward (1994). Chaos in Dynamical Systems. Cambridge University Press. ISBN 0-521-43799-7.