Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Characterization of inert actions on periodic points. Part II

Characterization of inert actions on periodic points. Part II Forum Math. 12 (2000), 671±712 ( de Gruyter 2000 K. H. Kim, F. W. Roush, and J. B. Wagoner (Communicated by Michael Brin) 1 Introduction We will prove the following theorem stated in [KRW3], thereby completing the third and ®nal step in characterizing inert actions on ®nite sets of periodic points of a primitive subshift of ®nite type XA Y sA constructed from a nonnegative integral matrix A. See [KRW1, KRW2, KRW3] for de®nitions and notation. SGCC Theorem. Assume A is primitive and that h 2 is a positive integer such that for every integer s h there is at least one periodic point of period exactly s. Let be in AutsA jPh . Let g yk GYk for 2 k h, and let osk OSk for 1 k h. Assume that the sign-gyration-compatibility-condition gyk oska2 i 0 ib0 holds for 2 k h. Then there is an element z in InertsA such that GYk z g yk OSk z osk for 2 k h for 1 k h While the method of proof is somewhat similar to the one used in proving the GY Theorem and OS Theorem of [KRW3], a new technique called the Enlargement Method http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Characterization of inert actions on periodic points. Part II

Kim, K. H.; Roush, F. W.; Wagoner, J. B.
Forum Mathematicum , Volume 12 (6) – Sep 6, 2000
Download PDF
42 pages

Loading next page...
 
/lp/de-gruyter/characterization-of-inert-actions-on-periodic-points-part-ii-rUuRlxz9Y0

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
Copyright © 2000 by Walter de Gruyter GmbH & Co. KG
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.2000.023
Publisher site
See Article on Publisher Site

Abstract

Forum Math. 12 (2000), 671±712 ( de Gruyter 2000 K. H. Kim, F. W. Roush, and J. B. Wagoner (Communicated by Michael Brin) 1 Introduction We will prove the following theorem stated in [KRW3], thereby completing the third and ®nal step in characterizing inert actions on ®nite sets of periodic points of a primitive subshift of ®nite type XA Y sA constructed from a nonnegative integral matrix A. See [KRW1, KRW2, KRW3] for de®nitions and notation. SGCC Theorem. Assume A is primitive and that h 2 is a positive integer such that for every integer s h there is at least one periodic point of period exactly s. Let be in AutsA jPh . Let g yk GYk for 2 k h, and let osk OSk for 1 k h. Assume that the sign-gyration-compatibility-condition gyk oska2 i 0 ib0 holds for 2 k h. Then there is an element z in InertsA such that GYk z g yk OSk z osk for 2 k h for 1 k h While the method of proof is somewhat similar to the one used in proving the GY Theorem and OS Theorem of [KRW3], a new technique called the Enlargement Method

Journal

Forum Mathematicum – de Gruyter

Published: Sep 6, 2000

There are no references for this article.