Curves of fixed points of trace maps

• Autores: Stephen Humphries, Anthony Manning
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 4, 2007, págs. 1167-1198
• Idioma: inglés
• DOI: 10.1017/s0143385707000016
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• Resumen

  • 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 $E_1$.