Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Divisibility constraints on degrees of factor maps

Author: Paul Trow
Journal: Proc. Amer. Math. Soc. 113 (1991), 755-760
MSC: Primary 28D05
MathSciNet review: 1056686
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the degree of a finite-to-one factor map $ f:{\sum _A} \to {\sum _B}$ between shifts of finite type is constrained by the factors of $ {\chi _A}$ and $ {\chi _B}$. A special case of these constraints is that if $ ^*B$, then the degree of $ f$ is a unit in $ \mathbb{Z}[1/{\det ^*}B]$ (where $ ^*A$ is the rank of the Jordan form away from 0 of $ A$, and $ {\det ^*}B$ is the determinant of the Jordan form away from 0 of $ B$).

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

  • [AM] R. L. Adler and B. Marcus, Topological entropy and equivalence of dynamical systems, Mem. Amer. Math. Soc., no. 219, Amer. Math. Soc., Providence, RI, 1979. MR 533691 (83h:28027)
  • [B] M. Boyle, Constraints on the degree of a sofic homomorphism and the induced multiplication of measures on unstable sets, Israel J. Math. 53 (1986), 52-68. MR 861897 (88d:28025)
  • [CP] E. Coven and M. Paul, Sofic systems, Israel J. Math. 20 (1975), 165-177. MR 0383379 (52:4260)
  • [H] G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3 (1969), 320-375. MR 0259881 (41:4510)
  • [HK] K. Hoffman and R. Kunze, Linear algebra, Prentice-Hall, Englewood Cliffs, NJ, 1961. MR 0125849 (23:A3146)
  • [K] B. Kitchens, An invariant for continuous factors of Markov chains, Proc. Amer. Math. Soc. 83 (1981), 825-828. MR 630029 (82k:28021)
  • [KMT] B. Kitchens, B. Marcus, and P. Trow, Eventual factor maps and compositions of closing maps, Ergodic Theory Dynamical Systems (to appear). MR 1101086 (92b:58062)
  • [PT] W. Parry and S. Tuncel, Classification problems in ergodic theory, London Math. Soc. Lecture Notes Ser., vol. 67, Cambridge University Press, Cambridge and New York, 1982. MR 666871 (84g:28024)
  • [T1] P. Trow, Degrees of constant-to-one factor maps, Proc. Amer. Math. Soc. 103 (1988), 184-188. MR 938666 (89m:28030)
  • [T2] -, Degrees of finite-to-one factor maps, Israel J. Math. (to appear). MR 1088817 (91m:58052)
  • [W] R. F. Williams, Classification of one-dimensional attractors, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, RI, 1970, 341-361. MR 0266227 (42:1134)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28D05

Retrieve articles in all journals with MSC: 28D05

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society