### On Dominated Extension of Continuous Affine Functions on Split Faces.

Tage Bai Andersen (1971)

Mathematica Scandinavica

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Tage Bai Andersen (1971)

Mathematica Scandinavica

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Józef Joachim Telega (1977)

Annales Polonici Mathematici

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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.

Cruceanu, Vasile (2005)

Balkan Journal of Geometry and its Applications (BJGA)

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Joachim Schmid (1995)

Manuscripta mathematica

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Varga, Adrienn (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Takashi Sano (1999)

Banach Center Publications

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We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.

Aldo J. Lazar (1968)

Mathematica Scandinavica

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Udo Simon, An-Mi Li, Luc Vrancken (1991)

Mathematische Zeitschrift

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John Smillie (1981)

Inventiones mathematicae

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Karáné, G.S. (1994)

Beiträge zur Algebra und Geometrie

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Takashi Kurose (1990)

Mathematische Zeitschrift

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Bach, Andrea K. (1997)

Beiträge zur Algebra und Geometrie

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Papi, Paolo (1997)

The Electronic Journal of Combinatorics [electronic only]

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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...

Michał Sadowski (1990)

Colloquium Mathematicae

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