Invariant manifold
Encyclopedia
In dynamical systems, a branch of mathematics
, an invariant manifold is a topological manifold
that is invariant under the action of the dynamical system. An example is the stable manifold
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an invariant manifold is a topological manifold
Topological manifold
In mathematics, a topological manifold is a topological space which looks locally like Euclidean space in a sense defined below...
that is invariant under the action of the dynamical system. An example is the stable manifold
Stable manifold
In mathematics, and in 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 notions embodied in the idea of an attractor or repellor...
.