Stable manifold theorem information

the study of dynamical systems and differential equations, the stable manifold theorem is an important result about the structure of the set of orbits...

particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general...

direction defines the stable manifold, the stretching direction defining the unstable manifold, and the neutral direction is the center manifold. While geometrically...

manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold,...

separability of the classes, and measures of geometry, topology, and density of manifolds. For non-binary classification problems, instance hardness is a bottom-up...

equilibrium point (x*, y*) is called the community matrix. By the stable manifold theorem, if one or both eigenvalues of A {\displaystyle \mathbf {A} } have...

non-embedded) manifold with a given stable trivialisation of the tangent bundle. A related notion is the concept of a π-manifold. A smooth manifold M {\displaystyle...

the annulus theorem in dimensions n ≥ 5 {\displaystyle n\geq 5} . It was also employed in further investigations of topological manifolds with Laurent...

mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are formed by adding structure to a topological manifold (e.g. differentiable...

Alternately, conservative systems are those to which the Poincaré recurrence theorem applies. An important special case of conservative systems are the measure-preserving...

a branch of mathematics, the stable normal bundle of a differentiable manifold is an invariant which encodes the stable normal (dually, tangential) data...

intimately related to the transversality properties of smooth manifolds—see Thom transversality theorem. By reversing this construction, John Milnor and Sergei...

eigenvalues of the community matrix have negative real part, then by the stable manifold theorem the system converges to a limit point. Since the determinant is...

equations, vector fields on smooth manifolds and flows generated by them, and diffeomorphisms. Structurally stable systems were introduced by Aleksandr...

Rokhlin's theorem that the signature of a compact smooth spin 4-manifold is divisible by 16. Stable homotopy groups of spheres are used to describe the group...

equations. Attractor Hyperbolic set Periodic point Self-oscillation Stable manifold Thomas, Jeffrey P.; Dowell, Earl H.; Hall, Kenneth C. (2002), "Nonlinear...

studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness...

Kähler manifold. The theorem can be considered a vast generalisation of the Narasimhan–Seshadri theorem which defines a correspondence between stable vector...

version of the transversality theorem. Let f : X → Y {\displaystyle f\colon X\rightarrow Y} be a smooth map between smooth manifolds, and let Z {\displaystyle...

Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic. The only invariants of a symplectic manifold are global...