Skip to main content
SpringerLink
Log in

Classification of topologically conjugate affine mappings

  • BRIEF COMMUNICATIONS
  • Published:
Ukrainian Mathematical Journal Aims and scope

We consider affine mappings from ℝn into ℝn, n ≥ 1. We prove a theorem on the topological conjugacy of an affine mapping that has at least one fixed point to the corresponding linear mapping. We give a classification, up to topological conjugacy, for affine mappings from R into R and also for affine mappings from ℝn into ℝn, n > 1, having at least one fixed point and the nonperiodic linear part.

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

References

  1. N. H. Kuiper and J. W. Robbin, “Topological classification of linear endomorphisms,” Invent. Math., 19, 83–106 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  2. J. W. Robbin, “Topological conjugacy and structural stability for discrete dynamical systems,” Bull. Amer. Math. Soc., 78, No. 6, 923–952 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. E. Cappell and J. L. Shaneson, “Nonlinear similarity of matrices,” Bull. Amer. Math. Soc., New Ser., 1, No. 6, 899–902 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  4. S. E. Cappell and J. L. Shaneson, “Nonlinear similarity,” Ann. Math., 113, 315–355 (1981).

    Article  MathSciNet  Google Scholar 

  5. S. E. Cappell and J. L. Shaneson, “Nonlinear similarity and differentiability,” Commun. Pure Appl. Math., 38, 697–706 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  6. W. C. Hsiang and W. Pardon, “When are topologically equivalent orthogonal transformations linearly equivalent,” Invent. Math., 68, 275–316 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  7. I. Madsen and M. Rothenberg, “Classifying G spheres,” Bull. Amer. Math. Soc., New Ser., 7, No. 1, 223–226 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Schultz, “On the topological classification of linear representations,” Topology, 16, 263–269 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Palis, Jr., and W. de Melo, Geometric Theory of Dynamical Systems. An Introduction, Springer, New York (1982).

    MATH  Google Scholar 

  10. S. E. Cappell and J. L. Shaneson, “Linear algebra and topology,” Bull. Amer. Math. Soc., New Ser., 1, No. 4, 685–687 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  11. G. P. Pelyukh and A. N. Sharkovskii, Introduction to the Theory of Functional Equations [in Russian], Naukova Dumka, Kiev (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    T. V. Budnyts’ka

Authors
  1. T. V. Budnyts’ka
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 134–139, January, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Budnyts’ka, T.V. Classification of topologically conjugate affine mappings. Ukr Math J 61, 164–170 (2009). https://doi.org/10.1007/s11253-009-0188-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-009-0188-y

Keywords

Search

Navigation