# 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

Forum Mathematicum, Volume 12 (6) – Sep 6, 2000
42 pages

/lp/de-gruyter/characterization-of-inert-actions-on-periodic-points-part-ii-rUuRlxz9Y0
Publisher
de Gruyter
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 Mathematicumde Gruyter

Published: Sep 6, 2000

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