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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
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Abstract

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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.

Information

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

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