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...

approximating integrals Maximum and minimum Derivative test Hyperbolic equilibrium point Hyperbolic geometry Minimax theorem Max–min inequality Monkey saddle...

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

local behaviour of dynamical systems in the neighbourhood of a hyperbolic equilibrium point. It asserts that linearisation—a natural simplification of the...

A point of negative Gaussian curvature on a smooth surface A hyperbolic equilibrium point of a dynamical system This disambiguation page lists mathematics...

eigenvalue. An equilibrium point is hyperbolic if none of the eigenvalues have zero real part. If all eigenvalues have negative real parts, the point is stable...

hyperbolic then there exists a Riemannian metric for which c = 1 — such a metric is called adapted. Hyperbolic equilibrium point p is a fixed point,...

Hydrostatic equilibrium, the state of a system in which compression due to gravity is balanced by a pressure gradient force Hyperbolic equilibrium point, a mathematical...

of the Jacobian matrix evaluated at a hyperbolic equilibrium point to determine the nature of that equilibrium. This is the content of the linearization...

point Hyperbolic equilibrium point Ideal point Inflection point Integral point Isolated point Generic point Heegner point Lattice hole, Lattice point Lebesgue...

an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolicity to non-autonomous systems. If x ˙ = A ( t ) x {\displaystyle...

system whose non-wandering set consists of finitely many hyperbolic equilibrium points and hyperbolic periodic orbits and satisfying a transversality condition...

magnetohydrodynamics, thermodynamics, and more generally systems described by hyperbolic partial differential equations involving both spatial and time derivatives...

(/ləˈɡrɑːndʒ/; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the gravitational influence of two massive...

center-unstable, sub-center, slow, and fast subspaces. If the equilibrium point is hyperbolic (that is, all eigenvalues of the linearization have nonzero...

point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium...

homoclinic orbit is a path through phase space which joins a saddle equilibrium point to itself. More precisely, a homoclinic orbit lies in the intersection...

model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines...

bifurcation point) there is exactly one equilibrium point. At this point the fixed point is no longer hyperbolic. In this case the fixed point is called...

this is when the universe reaches thermodynamic equilibrium. If the curvature of the universe is hyperbolic or flat, or if dark energy is a positive cosmological...

into the logistic distribution. Geometrically, the hyperbolic tangent function is the hyperbolic angle on the unit hyperbola x 2 − y 2 = 1 {\displaystyle...

occurs when the partial pressure of vapor of a substance is less than the equilibrium vapor pressure. For example, due to constantly decreasing pressures,...

modelling non-equilibrium real gas effects is radiative heat flux. If a vehicle is entering an atmosphere at very high speed (hyperbolic trajectory, lunar...

hanging rope. Mathematically, the catenary curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the...

satisfied if the equilibrium is at the minimum point of the average total cost curve. This is again the case for the long run equilibrium of perfect competition...

with the geometry of nearly spherical surfaces: umbilical point. Thom proposed that the hyperbolic umbilic catastrophe modeled the breaking of a wave and...

the case (for example) of a body passing the primary on a parabolic or hyperbolic trajectory. The rigid-body Roche limit is a simplified calculation for...

only if the following two conditions hold: All equilibrium points and periodic orbits are hyperbolic. There are no saddle connections. The same statement...

a fixed point having a Floquet multiplier with modulus equal to one. In both cases, the equilibrium is non-hyperbolic at the bifurcation point. The topological...

increasing oscillations, chaotic behavior or other divergences from equilibrium. System parameters will typically accelerate towards extreme values,...