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Curves of fixed points of trace maps

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Humphries, Stephen and Manning, Anthony. (2007) Curves of fixed points of trace maps. Ergodic Theory and Dynamical Systems, Vol.27 (No.4). pp. 1167-1198. ISSN 0143-3857

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Official URL: http://dx.doi.org/10.1017/S0143385707000016

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 $E_1$.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Invariants, Dynamics, Diffeomorphisms
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Date:	22 June 2007
Volume:	Vol.27
Number:	No.4
Page Range:	pp. 1167-1198
Identification Number:	10.1017/S0143385707000016
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/673