On affine geometric product objects
Józef Joachim Telega (1977)
Annales Polonici Mathematici
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Józef Joachim Telega (1977)
Annales Polonici Mathematici
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John Smillie (1981)
Inventiones mathematicae
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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.
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.
Frans Keune (1975)
Inventiones mathematicae
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Jacob Eli Goodman, Alan Landman (1973)
Inventiones mathematicae
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Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Altmann, Klaus (1993)
Beiträge zur Algebra und Geometrie
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Udo Simon, An-Mi Li, Luc Vrancken (1991)
Mathematische Zeitschrift
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Varga, Adrienn (2008)
Banach Journal of Mathematical Analysis [electronic only]
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R. HARTSHORNE (1969/70)
Inventiones mathematicae
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Joachim Schmid (1995)
Manuscripta mathematica
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Christoph Bandt, Mathias Mesing (2009)
Banach Center Publications
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In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which...
T. Kambayashi (1979)
Inventiones mathematicae
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