Displaying similar documents to “On the algebraic structure on the jet prolongations of fibred manifolds”

An affine framework for analytical mechanics

Paweł Urbański (2003)

Banach Center Publications

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An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.

Affine bijections of C(X,I)

Janko Marovt (2006)

Studia Mathematica

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Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.

Affine structures on jet and Weil bundles

David Blázquez-Sanz (2009)

Colloquium Mathematicae

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Weil algebra morphisms induce natural transformations between Weil bundles. In some well known cases, a natural transformation is endowed with a canonical structure of affine bundle. We show that this structure arises only when the Weil algebra morphism is surjective and its kernel has null square. Moreover, in some cases, this structure of affine bundle passes to jet spaces. We give a characterization of this fact in algebraic terms. This algebraic condition also determines an affine...