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manuscripta mathematica

, Volume 21, Issue 2, pp 101–115 | Cite as

Über geschlossene affine Zwangläufe in der Ebene

  • Christoph Lübbert
Article

Abstract

We consider integral coverings y:
→{1,2,..,∞} of an affine plane
which occur when
is moved under a continuous periodic affine motionα(t):
. One can distinguish normal points × ∈
, i.e. γ is constant in a certain neighborhood of x, and singular points. If γ(x) is the number of times x passes through its orbit α(t)x all normal points x have γ(x)=1, and the set of all singular points consists of a number of isolated points and lines. If γ(x) is the tangent rotation number of the orbit of x all singular points lie on the moving pole curve.

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Literatur

  1. [1]
    BLASCHKE, W./MÜLLER, H.R.: Ebene Kinematik, München 1956.Google Scholar
  2. [2]
    BOL, G.: Projektive Differentialgeometrie I. Göttingen 1950.Google Scholar
  3. [3]
    DOUGLAS, V./HEIL, E./LÜBBERT, C.: Geradenfamilien, Enveloppen und Evoluten. Journal r.a.Math.283/284 (1976), 370–383.Google Scholar
  4. [4]
    HAMMER, P.C./SOBCZYK, A.: Planar line families I, II. Proc. Amer. Math. Soc.4 (1953) 226–233, 341–349.Google Scholar
  5. [5]
    HAYASHI, T.: Some geometrikal applikations of Fourier serien. Rend. Circ. Matem. Palermo,50 (1926), 96–102Google Scholar
  6. [6]
    KRASNOSELSKI, M.A./ PEROW, A.I./ POWOLOZKI, A.I./SABREJKO, P.P.: Vektorfelder in der Ebene. Berlin 1966.Google Scholar
  7. [7]
    LÜBBERT, C.: Symmetrieeigenschaften ebener periodischer Bewegungsvorgänge, ZAMM52 (1972) 311–314.Google Scholar
  8. [8]
    MORSE, M.: Topological methods in the theory of functions of a complex variable (Ann. of math. studies, Nr.15) Princeton University Press, 1947.Google Scholar
  9. [9]
    MÜLLER, H.R.: Bewegungsvorgänge mit mehrfach durchlaufenen Bahnkurven. Monatsh. Math.67 (1963) 326–334.Google Scholar
  10. [10]
    WHITNEY, H.: On regular closed curves in the plane. Compos. math.4 (1937) 276–284.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Christoph Lübbert
    • 1
  1. 1.Fachbereich MathematikTechnische HochschuleDarmstadtBundesrepublik Deutschland

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