- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:57
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
1
2007
2
Denominator bounds in Thompson-like groups and flows
Danny
Calegari
California Institute of Technology, PASADENA, UNITED STATES
Thompson's group, rotation number, rationality
Let T denote Thompson's group of piecewise 2-adic linear homeomorphisms of the circle. Ghys and Sergiescu showed that the rotation number of every element of T is rational, but their proof is very indirect. We give here a short, direct proof using train tracks, which generalizes to elements of PL+(S1) with rational break points and derivatives which are powers of some fixed integer, and also to certain flows on surfaces which we call Thompson-like. We also obtain an explicit upper bound on the smallest period of a fixed point in terms of data which can be read off from the combinatorics of the homeomorphism.
Dynamical systems and ergodic theory
General
101
109
10.4171/GGD/6
http://www.ems-ph.org/doi/10.4171/GGD/6