Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Curves of period two points for trace maps


Authors: Stephen P. Humphries and Anthony Manning
Journal: Trans. Amer. Math. Soc. 367 (2015), 5721-5751
MSC (2010): Primary 37C25, 37D40, 37E99; Secondary 42C05
DOI: https://doi.org/10.1090/S0002-9947-2014-06367-8
Published electronically: October 10, 2014
MathSciNet review: 3347188
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider an infinite family of trace maps $ \alpha _n$ and their action on $ \mathbb{R}^3$. Trace maps fix certain invariant surfaces, and in an earlier paper we found that the fixed points for $ \alpha _n$ on one such surface were joined in pairs by curves of fixed points, thus determining a `duality' for such fixed points. We now extend this idea to determine the duality for all the points of period $ 2$ that lie in the planes $ x=\pm y$ and for certain others that do not.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 37C25, 37D40, 37E99, 42C05

Retrieve articles in all journals with MSC (2010): 37C25, 37D40, 37E99, 42C05


Additional Information

Stephen P. Humphries
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: steve@mathematics.byu.edu

Anthony Manning
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: A.Manning@warwick.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-2014-06367-8
Keywords: Trace map, periodic point, curve of fixed points, Chebyshev polynomial, area preserving map
Received by editor(s): August 13, 2013
Published electronically: October 10, 2014
Article copyright: © Copyright 2014 American Mathematical Society

American Mathematical Society