Resumen de Fixed points and periodic points of orientation-reversing planar homeomorphisms

J. P. Boronski

• Two results concerning orientation-reversing homeomorphisms of the plane are proved. Let be an orientation-reversing 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 2-periodic orbit in , or there is a 2-periodic component of . The second result is based on a recent result of M. Bonino concerning linked periodic orbits of orientation-reversing homeomorphisms of the 2-sphere . These results generalize to orientation-reversing homeomorphisms of .