Skip to main content
SpringerLink
Log in

Über geschlossene affine Zwangläufe in der Ebene

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literatur

  1. BLASCHKE, W./MÜLLER, H.R.: Ebene Kinematik, München 1956.

  2. BOL, G.: Projektive Differentialgeometrie I. Göttingen 1950.

  3. DOUGLAS, V./HEIL, E./LÜBBERT, C.: Geradenfamilien, Enveloppen und Evoluten. Journal r.a.Math.283/284 (1976), 370–383.

    Google Scholar 

  4. HAMMER, P.C./SOBCZYK, A.: Planar line families I, II. Proc. Amer. Math. Soc.4 (1953) 226–233, 341–349.

    Google Scholar 

  5. HAYASHI, T.: Some geometrikal applikations of Fourier serien. Rend. Circ. Matem. Palermo,50 (1926), 96–102

    Google Scholar 

  6. KRASNOSELSKI, M.A./ PEROW, A.I./ POWOLOZKI, A.I./SABREJKO, P.P.: Vektorfelder in der Ebene. Berlin 1966.

  7. LÜBBERT, C.: Symmetrieeigenschaften ebener periodischer Bewegungsvorgänge, ZAMM52 (1972) 311–314.

    Google Scholar 

  8. MORSE, M.: Topological methods in the theory of functions of a complex variable (Ann. of math. studies, Nr.15) Princeton University Press, 1947.

  9. MÜLLER, H.R.: Bewegungsvorgänge mit mehrfach durchlaufenen Bahnkurven. Monatsh. Math.67 (1963) 326–334.

    Google Scholar 

  10. WHITNEY, H.: On regular closed curves in the plane. Compos. math.4 (1937) 276–284.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule, Schloßgartenstr. 7, 6100, Darmstadt, Bundesrepublik Deutschland

    Christoph Lübbert

Authors
  1. Christoph Lübbert
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lübbert, C. Über geschlossene affine Zwangläufe in der Ebene. Manuscripta Math 21, 101–115 (1977). https://doi.org/10.1007/BF01168014

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01168014

Search

Navigation