Generalizing the rotation interval to vertex maps on graphs
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- by Chris Bernhardt and P. Christopher Staecker PDF
- Trans. Amer. Math. Soc. 367 (2015), 4235-4252 Request permission
Abstract:
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a rotation element is defined in terms of the fundamental group. A number of results are proved about the rotation elements associated to periodic points in a given edge of the graph. Most of the results show that the existence of two periodic points with certain rotation elements will imply an infinite family of other periodic points with related rotation elements. These results for periodic points can be considered as generalizations of the rotation interval for degree one maps of the circle.References
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Additional Information
- Chris Bernhardt
- Affiliation: Department of Mathematics and Computer Science, Fairfield University, Fairfield, Connecticut 06824
- Email: cbernhardt@fairfield.edu
- P. Christopher Staecker
- Affiliation: Department of Mathematics and Computer Science, Fairfield University, Fairfield, Connecticut 06824
- Email: cstaecker@fairfield.edu
- Received by editor(s): September 21, 2012
- Received by editor(s) in revised form: February 14, 2013, May 27, 2013, and June 1, 2013
- Published electronically: September 5, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 4235-4252
- MSC (2010): Primary 37E15, 37E25, 37E45
- DOI: https://doi.org/10.1090/S0002-9947-2014-06229-6
- MathSciNet review: 3324926