Semiconjugacies to angle-doubling
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- by Philip Boyland PDF
- Proc. Amer. Math. Soc. 134 (2006), 1299-1307 Request permission
Abstract:
A simple consequence of a theorem of Franks says that whenever a continuous map, $g$, is homotopic to angle-doubling on the circle, it is semiconjugate to it. We show that when this semiconjugacy has one disconnected point inverse, then the typical point in the circle has a point inverse with uncountably many connected components. Further, in this case the topological entropy of $g$ is strictly larger than that of angle-doubling, and the semiconjugacy has unbounded variation. An analogous theorem holds for degree-$D$ circle maps with $D > 2$.References
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Additional Information
- Philip Boyland
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32605-8105
- Email: boyland@math.ufl.edu
- Received by editor(s): November 15, 2004
- Published electronically: October 5, 2005
- Communicated by: Michael Handel
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1299-1307
- MSC (2000): Primary 37E10
- DOI: https://doi.org/10.1090/S0002-9939-05-08381-4
- MathSciNet review: 2199172