| 41. | I ) reproduction of the Poisson brackets ( of the diffeomorphism constraints in the case of general relativity ).
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| 42. | Not every manifold admits an Anosov diffeomorphism; for example, there are no such diffeomorphisms on the sphere.
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| 43. | It was proved that any other Anosov diffeomorphism on a torus is topologically conjugate to one of this kind.
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| 44. | Suppose we have a diffeomorphism " T " which preserves the Lebesgue measure and is C 3.
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| 45. | One can also make this operation work in the category, and then the result is unique up to diffeomorphism.
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| 46. | Thus the exponential map is a diffeomorphism from \ mathfrak { p } onto the space of positive definite matrices.
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| 47. | The notion of a diffeomorphism of " S " is redefined with respect to this modified differentiable structure.
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| 48. | For example, it provides a natural way to express the direct link between spontaneous Lorentz breaking and diffeomorphism breaking.
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| 49. | Composing the original diffeomorphism with the inverse of " f " then yield zero as the Beltrami coefficient.
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| 50. | Therefore, one may employ big words : every one-loop filter is a diffeomorphism of every other one.
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