Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T00:56:36.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Real analytic actions of SL (2, ℝ) on a surface

Published online by Cambridge University Press:  19 September 2008

Dennis C. Stowe
Dennis C. Stowe
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305, USA
Rights & Permissions [Opens in a new window]

Abstract

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.

Real analytic actions of connected Lie groups locally isomorphic to SL (2, ℝ) on compact surfaces, possibly with boundary, are classified up to topological conjugacy and up to real analytic conjugacy. Finite dimensional universal unfoldings of the real analytic conjugacy relation are also constructed. These are local transversals to the conjugacy classes in the space of actions. Sometimes the unfolding is a variety but not a manifold, and thus the space of actions is not naturally modelled on a vector space. We find many rigid actions and some unexpected bifurcation.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 3 , September 1983 , pp. 447 - 499
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

[1]Guillemin, V. & Sternberg, S.. Remarks on a paper of Hermann. Trans. Amer. Math. Soc. 130 (1968), 110–116.CrossRefGoogle Scholar
[2]Hermann, R.. The formal linearization of a semisimple Lie algebra of vector fields about a singular point. Trans. Amer. Math. Soc. 130 (1968), 105–109.CrossRefGoogle Scholar
[3]Hirsch, M.. Differential Topology. Springer-Verlag: Berlin and New York, 1976.CrossRefGoogle Scholar
[4]Koppell, N.. Commuting diffeomorphisms. In Global Analysis, Proc. Symp. Pure Math., vol. 14, p. 165–184. Amer. Math. Soc., Providence, R.I., 1970.Google Scholar
[5]Palais, R.. Equivalence of nearby differentiable actions of a compact group. Bull. Amer. Math. Soc. 67 (1961), 362–364.CrossRefGoogle Scholar
[6]Robbin, J.. On an example in the theory of unfolding of discrete dynamical systems. To appear.Google Scholar
[7]Smale, S.. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747–817.CrossRefGoogle Scholar
[8]Stowe, D.. The stationary set of a group action. Proc. Amer. Math. Soc. 79 (1980), 139–146.CrossRefGoogle Scholar