Fixed points and periodic points of orientationreversing planar homeomorphisms
Author:
J. P. Boronski
Journal:
Proc. Amer. Math. Soc. 138 (2010), 37173722
MSC (2010):
Primary 55M20; Secondary 54F15, 54H25, 58C30
Published electronically:
April 13, 2010
MathSciNet review:
2661570
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Abstract: Two results concerning orientationreversing homeomorphisms of the plane are proved. Let be an orientationreversing planar homeomorphism with a continuum invariant (i.e. ). First, suppose there are at least bounded components of that are invariant under . Then there are at least components of the fixed point set of in . This provides an affirmative answer to a question posed by K. Kuperberg. Second, suppose there is a periodic orbit in with . Then there is a 2periodic orbit in , or there is a 2periodic component of . The second result is based on a recent result of M. Bonino concerning linked periodic orbits of orientationreversing homeomorphisms of the 2sphere . These results generalize to orientationreversing homeomorphisms of .
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Additional Information
J. P. Boronski
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849
Email:
boronjp@auburn.edu
DOI:
http://dx.doi.org/10.1090/S0002993910103608
Keywords:
Fixed point,
periodic point,
planar homeomorphism,
continuum
Received by editor(s):
August 8, 2009
Received by editor(s) in revised form:
December 31, 2009
Published electronically:
April 13, 2010
Additional Notes:
The author was supported in part by NSF Grant #DMS0634724
Dedicated:
Dedicated to the memory of Professor Andrzej Lasota (1932–2006)
Communicated by:
Bryna Kra
Article copyright:
© Copyright 2010
American Mathematical Society
