|
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." Several properties hold about a neighborhood of a hyperbolic point, notably * 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. == Maps == If ''T'' : R''n'' → R''n'' is a ''C''1 map and ''p'' is a fixed point then ''p'' is said to be a hyperbolic fixed point when the Jacobian matrix ''DT''(''p'') has no eigenvalues on the unit circle. One example of a map that its only fixed point is hyperbolic is the Arnold Map or cat map: : Since the eigenvalues are given by : : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「hyperbolic equilibrium point」の詳細全文を読む スポンサード リンク
|