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