Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T00:55:35.537Z Has data issue: false hasContentIssue false
  • English
  • Français

R-isomorphisms of Transformation Groups and Prolongations

Published online by Cambridge University Press:  20 November 2018

Larry King
Larry King*
Affiliation:
University of Massachusetts, Amherst, Massachusetts
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [8] the notion of a reparameterizing isomorphism of transformation groups, henceforth called an R-isomorphism, is introduced generalizing Ura's type-2 isomorphism (see [13]). We have shown [8] that an R-isomorphism is weaker than a transformation group isomorphism. For example, although R-isomorphisms preserve pointwise almost periodicity and minimality they do not preserve the existence of slices [7] or almost periodicity. This suggests that R-isomorphisms might be a useful classification tool in topological dynamics.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 338 - 344
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Ahmad, Shair, Dynamical systems of characteristic 0+, Pacific J. Math. 32 (1970), 561–574.Google Scholar
2. Bhatia, N. P. and Szegö, G. P.,Dynamical systems: Stability theory and applications, Lecture Notes in Math. 35 (Springer-Verlag, Berlin-Heidelberg, 1967).Google Scholar
3. Dugundji, J., Topology (Allyn and Bacon, Inc., Boston, 1966).Google Scholar
4. Gottschalk, W. H. and Hedlund, G. A., Topological dynamics (Amer. Math.Soc, Providence, R.L, 1955).Google Scholar
5. Hajek, O., Prolongations in topological dynamics, Seminar on differential equations and Dynamical systems II, Lecture Notes in Math. 144 (Springer-Ver lag, Berlin-Heidelberg, 1970), 79–89.Google Scholar
6. Hanson, T. H. McH., Actions of a locally compact group with zero, Can. J. Math. 23 (1971), 413–420.Google Scholar
7. King, L., Slices in transformation groups, Trans. Amer. Math. Soc. 147 (1970), 381–388.Google Scholar
8. King, L., Types of isomorphisms of transformation groups, Math. Systems Theory 5 (1971), 376–382.Google Scholar
9. King, L., Actions of a noncompactsemigroup with zero, Semigroup Forum 4 (1972), 224–231.Google Scholar
10. Markus, L., Parallel dynamical systems, Topology 8 (1969), 47–57.Google Scholar
11. Palais, R. S., On the existence of slices for actions of noncompact Lie groups, Ann. of Math. 73 (1961), 295–323.Google Scholar
12. Palais, R. S., The classification of G-spaces, Mem. Amer. Math. Soc. 36 (1960), 1–45.Google Scholar
13. Ura, T., Local isomorphisms and local parallelizability in dynamical systems theory, Math. Systems Theory 3 (1969), 1–16.Google Scholar