Vol. 39, No. 1, 1971

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Reversible homeomorphisms of the real line

Arnold Barry Calica

Vol. 39 (1971), No. 1, 79–87
Abstract

Let G be the group of germs of Ck local homeomorphisms of the real line which fix the origin and have nonzero derivative there. In this paper the possibility of factoring an element of G which is conjugate to its inverse into the product of two involutions is investigated. It is shown that it is always possible to do this in the analytic case and not always possible in the continuous case. In the intermediate cases several necessary and sufficient conditions are developed for determining whether or not such a factorization is possible. Included is a construction which allows one to determine an explicit factorization. Indication is given of the application of this material to the same problem in higher dimensions. This work is related to some material in Dynamics.

Mathematical Subject Classification 2000
Primary: 54C05
Secondary: 58C05
Milestones
Received: 22 May 1970
Published: 1 October 1971
Authors
Arnold Barry Calica