diffeomorphism
1
9.9
- noun
- /ˌdɪfɪoʊˈmɔrfɪzəm/
- Specialized
- In differential geometry, a diffeomorphism is a function that is both smooth and has a smooth inverse between two manifolds.
Examples
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On differentiable manifolds, such a diffeomorphism may be defined which keeps everything outside a certain compact subset—"the hole"—identical, but changes what is inside the hole.
Academic text (1998) -
Indeed, the two Action integrals (3) and (9) are conformally related, but it is important to mention that g and the omitted formula are in principle two different metrics, in the sense that there does not necessarily exist a space-time diffeomorphism linking the two space-times.
Academic text (2018) -
In these cases, the monadic realm remains ontologically and metaphysically unaltered. All other diffeomorphisms would "produce" another monadic-perceptual realm.
Academic text (1998) -
Definition 3. System (19) is said to be (locally) non-regular static feedback-linearizable if it can be transformed into via state feedbacks with a ?(0) = 0, ?(x): mk, k<m, and a state space diffeomorphism.
Academic text (2010) -
Although the solutions of the conformal equivalent theories commute through the conformal transformation (24), the physical and geometrical properties of the solutions can be extremely different due to the fact that a conformal transformation cannot in general correspond to a diffeomorphism linking the two line elements.
Academic text (2018) -
When studying the shapes of surfaces, mathematicians often use a diffeomorphism to relate different geometric structures.
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To analyze the flow of a liquid, engineers apply a diffeomorphism to model how the fluid moves smoothly between various shapes.
Surface Forms
Morphology
Etymology
Diffeomorphism starts with diff- (as in 'different', suggesting 'change') and ends with -morphism (a root meaning 'form' or 'shape'). So a diffeomorphism is a smooth, reversible change of form that turns one space into another and can be undone.