The charts (homeomorphisms) that make up any differentiable structure of a differentiable manifold are required to be such that the transition from one to another is differentiable.

Whitney showed that a differentiable manifold Mᵏ can be regularly mapped on the vector space R²ᵏ.

The phase space of a dynamical system will be taken to be a differentiable manifold.

In this chapter we introduce differentiable manifolds and smooth maps. A differentiable manifold' is a topological space on which there are defined coordinates allowing basic notions of differentiability.

Differentiable manifold

Meaning

Noun