Hyperbolic point information

In mathematics, a hyperbolic point is a certain kind of point, one of: A point in a hyperbolic geometry A point of negative Gaussian curvature on a smooth...

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 Euclid's parallel postulate.) The hyperbolic plane is a plane where every point is a saddle point. Hyperbolic plane geometry is also the geometry of...

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...

function being a hyperbola Hyperbolic equilibrium point, a fixed point that does not have any center manifolds Hyperbolic function, an analog of an ordinary...

In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers. Several qualitatively different ways of...

common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse...

period of the point) has no eigenvalue on the (complex) unit circle when computed at the point. Then a saddle point is a hyperbolic periodic point whose stable...

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...

of hyperbolic equations are "wave-like". If a disturbance is made in the initial data of a hyperbolic differential equation, then not every point of space...

In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in...

either an ellipse, or a single point (in the case of a section by a tangent plane). A paraboloid is either elliptic or hyperbolic. Equivalently, a paraboloid...

In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number...

In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three...

precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group...

In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane...

In hyperbolic geometry, an ideal point, omega point or point at infinity is a well-defined point outside the hyperbolic plane or space. Given a line l...

Riemann sphere (when complex numbers are mapped to each point). In the case of a hyperbolic space, each line has two distinct ideal points. Here, the...

A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a)...

dynamical systems theory, a subset Λ of a smooth manifold M is said to have a hyperbolic structure with respect to a smooth map f if its tangent bundle may be...

In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous...

hyperbola of the Dupin indicatrix through a hyperbolic point, or the unique asymptote through a parabolic point. An asymptotic direction is a direction along...

In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane { ( x , y )   :   x > 0 ,   y > 0   } = Q {\displaystyle...

In mathematics, hyperbolic trigonometry can mean: The study of hyperbolic triangles in hyperbolic geometry (traditional trigonometry is the study of triangles...

In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic...

In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than...

Hyperbolic theory may refer to: Hyperbolic geometry The theory of hyperbolic partial differential equations This disambiguation page lists mathematics...

the ellipse. In particular, the indicatrix of an umbilical point is a circle. For hyperbolic points, where the Gaussian curvature is negative, the intersection...