#manifold
5 concepts
Concepts
Manifold
A manifold is a topological space locally resembling Euclidean space. Smooth manifolds additionally have differentiable structure.
Manifold
Topological space locally resembling Euclidean space. Generalization of surfaces
Tangent Space
Vector space of all possible "directions" at a point on manifold
Center Manifold
An invariant manifold tangent to neutral directions (zero eigenvalues) near a fixed point. Essential for bifurcation analysis and dimension reduction.
Lie Group
A group with smooth manifold structure. Group operations are differentiable, representing continuous symmetries.