Search results
Results from the WOW.Com Content Network
The birational point of view can afford to be careless about subsets of codimension 1. To have a moduli space as a scheme is on one side a question about characterising schemes as representable functors (as the Grothendieck school would see it); but geometrically it is more like a compactification question, as the stability criteria revealed.
The stability of fixed points of a system of constant coefficient linear differential equations of first order can be analyzed using the eigenvalues of the corresponding matrix. An autonomous system ′ =, where x(t) ∈ R n and A is an n×n matrix with real entries, has a constant solution =
In narratology, focalisation is the perspective through which a narrative is presented. [1] Coined by French narrative theorist Gérard Genette, his definition distinguishes between internal focalisation (first-person) and external focalisation (third-person, fixed on the actions of and environments around a character), with zero focalisation representing an omnisicent narrator. [2]
In several typical examples, the system has only one stable fixed point at low values of the parameter. A saddle-node bifurcation gives rise to a pair of new fixed points emerging, one stable and the other unstable, at a critical value of the parameter. The unstable solution can then form another saddle-node bifurcation with the initial stable ...
From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems.
In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed points of a transformation is also an invariant set.
The standard example is the action of C * on the plane C 2 defined as (,) = (,).The weight in the x-direction is 1 and the weight in the y-direction is -1.Thus by the Hilbert–Mumford criterion, a non-zero point on the x-axis admits 1 as its only weight, and a non-zero point on the y-axis admits -1 as its only weight, so they are both unstable; a general point in the plane admits both 1 and ...
A similar theory about the stability of fixed points can also be applied to periodic points. That is, a periodic point that attracts surrounding orbits is called an asymptotically stable periodic point, and a periodic point where the surrounding orbits move away is called an unstable periodic point.