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Curves of fixed points of trace maps

Published online by Cambridge University Press:  22 June 2007

STEPHEN HUMPHRIES  and
ANTHONY MANNING
STEPHEN HUMPHRIES
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA (e-mail: [email protected])
ANTHONY MANNING
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (e-mail: [email protected])
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Abstract

We study curves of fixed points for certain diffeomorphisms of ${\mathbb{R}}^3$ that are induced by automorphisms of a trace algebra. We classify these curves. There is a function $E$ which is invariant under all such trace maps and the level surfaces $E_t: E=t$ are invariant; a point of $E_t$ will be said to have level $t$. The surface $E_1$ is significant. Then most fixed points on $E_1$ are actually on a curve $\gamma$ of fixed points interior to $E_1$. We describe the possibilities for the other end of $\gamma$ on $E_1$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 4 , August 2007 , pp. 1167 - 1198
Copyright
2007 Cambridge University Press

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