manifold, stable manifold, unstable manifold, subcenter manifold and inertial manifold. Typically, although by no means always, invariant manifolds are...

to a nearby stable manifold and nearby unstable manifold. These three types of manifolds are three cases of an invariant manifold. Corresponding to the...

manifold has a topological invariant, its dimension. For most applications, a special kind of topological manifold, namely, a differentiable manifold...

a manifold in high-dimensional space, and the intrinsic variables of that manifold will represent the robot's position and orientation. Invariant manifolds...

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

given a bi-invariant Riemannian metric if and only if it is the product of a compact Lie group with an abelian Lie group. A Riemannian manifold (M, g) is...

respective manifolds. Hyperbolic 3-manifold Hyperbolic space Hyperbolization theorem Margulis lemma Normally hyperbolic invariant manifold Kapovich, Michael...

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

{\displaystyle K} of a two-dimensional Riemannian manifold ( M , g ) {\displaystyle (M,g)} is invariant under changes of the Riemannian metric g {\displaystyle...

pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate...

Kervaire invariant is an invariant of a framed ( 4 k + 2 ) {\displaystyle (4k+2)} -dimensional manifold that measures whether the manifold could be surgically...

signature is an integer invariant which is defined for an oriented manifold M of dimension divisible by four. This invariant of a manifold has been studied in...

In mathematics, the eta invariant of a self-adjoint elliptic differential operator on a compact manifold is formally the number of positive eigenvalues...

and especially gauge theory, Seiberg–Witten invariants are invariants of compact smooth oriented 4-manifolds introduced by Edward Witten (1994), using the...

acting on a real infinite-dimensional reflexive space. Invariant manifold Lomonosov's invariant subspace theorem Roman 2008, p. 73 §2 Roman 2008, p. 73...

Arf invariant is particularly applied in geometric topology, where it is primarily used to define an invariant of (4k + 2)-dimensional manifolds (singly...

is defined to be the invariant manifold on which the dynamics are slow compared to the dynamics off the manifold. The slow manifold in a particular problem...

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

networks of coupled oscillators where the system typically orbits in an invariant manifold with a chaotic attractor (where the peak trajectories are low), but...

framed links also give rise to invariants of 3-manifolds via the Dehn surgery construction. These invariants were discovered by Nicolai Reshetikhin and Vladimir...

mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere...

estimate the probability of rare events. Sritharan, S.S. (2019), Invariant Manifold Theory for Hydrodynamic Transition, Courier Dover Publications, ISBN 9780486828282...

conjecture, by Michael Hutchings to define an invariant of smooth three-manifolds, and by Lenhard Ng to define invariants of knots. It was also used by Yakov Eliashberg...

the classification of all smooth manifolds up to diffeomorphism. Since dimension is an invariant of smooth manifolds up to diffeomorphism type, this classification...

{M}}(t_{0})} yields an invariant manifold M ∈ P × I {\displaystyle {\mathcal {M}}\in {\mathcal {P}}\times {\mathcal {I}}} , invariant manifolds and their associated...

homeomorphism type of the manifold only depends on this intersection form, and on a Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } invariant called the Kirby–Siebenmann...

the (universal cover of the) free loop space of a symplectic manifold. SFH is invariant under Hamiltonian isotopy of the symplectomorphism. Here, nondegeneracy...

states. In mathematics, it has been used to calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons...

signature of a spin smooth manifold is divisible by 16, the definition of the Rokhlin invariant is deduced as follows: For 3-manifold N {\displaystyle N} and...

Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in...