concept of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised...

the center manifold. In other words, the 4-dimensional system collapses onto a 2-dimensional plane. Any solution starting off the center manifold will...

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

invariant manifold is a topological manifold that is invariant under the action of the dynamical system. Examples include the slow manifold, center manifold, stable...

point implies the existence of a local stable center manifold containing that fixed point. This manifold has dimension equal to the number of eigenvalues...

mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods...

respectively. Invariant manifold Center manifold Limit set Julia set Slow manifold Inertial manifold Normally hyperbolic invariant manifold Lagrangian coherent...

An inlet manifold or intake manifold (in American English) is the part of an internal combustion engine that supplies the fuel/air mixture to the cylinders...

(e.g. synergetics). Inertial manifolds may also appear as slow manifolds common in meteorology, or as the center manifold in any bifurcation. Computationally...

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

matrices, moments, local sensitivity and statistical diagnostics. Center manifold Hessian matrix Pushforward (differential) Differentiability at x implies...

transforms and invariant manifolds provide a sounder support for multiscale modelling (for example, see center manifold and slow manifold). As an example for...

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow...

Mathematically speaking, the dynamics has a center manifold, or more precisely a near center manifold. In addition, it has been found that the stellar...

In mathematics, a spherical 3-manifold M is a 3-manifold of the form M = S 3 / Γ {\displaystyle M=S^{3}/\Gamma } where Γ {\displaystyle \Gamma } is a finite...

known as manifold learning, is any of various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with...

Hyperbolic equilibrium point, a fixed point that does not have any center manifolds Hyperbolic function, an analog of an ordinary trigonometric or circular...

quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than the one for complex manifolds due in...

the center manifold is generated by the parabolic transformations, the unstable manifold by the hyperbolic transformations, and the stable manifold by...

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...

used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the...

A normally hyperbolic invariant manifold (NHIM) is a natural generalization of a hyperbolic fixed point and a hyperbolic set. The difference can be described...

introduced, such as monotonicity of a frequency function and the use of a center manifold to perform a more intricate blow-up procedure. A streamlined and more...

speeds, the valve was opened, diverting the incoming air into the center of the manifold. The shorter runners resulted in improved horsepower. Passenger...

mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally...

The Popov criterion and the circle criterion for absolute stability Center manifold theorem Small-gain theorem Passivity analysis Control design techniques...

and algorithmic development include: Analytical modeling Center manifold and slow manifold theory Continuum modeling Discrete modeling Network-based...

In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the...

clamp and bracket Exhaust flange gasket Exhaust gasket Exhaust manifold Exhaust manifold gasket Exhaust pipe Heat shield Heat sleeving and tape Resonator...

definitions given below. Connection Curvature Metric space Riemannian manifold See also: Glossary of general topology Glossary of differential geometry...