differentiable manifold

Definitions

1. 1

   A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do…

   A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;

   • 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 R#123;2k#125;.
   • The phase space of a dynamical system will be taken to be a differentiable manifold.

The neighborhood