Degrees of constant-to-one factor maps

Author:
Paul Trow

Journal:
Proc. Amer. Math. Soc. **103** (1988), 184-188

MSC:
Primary 28D05

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938666-4

MathSciNet review:
938666

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a constant-to-one endomorphism of degree , of a sub-shift of finite type . If is a prime dividing , then divides every nonleading coefficient of , the characteristic polynomial for . Further constraints are given for the possible degrees of a constant-to-one factor map between subshifts of finite type.

**[A-M]**R. L. Adler and B. Marcus,*Topological entropy and equivalence of dynamical systems*, Mem. Amer. Math. Soc., vol. 20, no. 219, 1979. MR**533691 (83h:28027)****[B1]**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)****[B2]**-, personal communication.**[H]**G. A. Hedlund,*Endomorphisms and automorphisms of the shift dynamical system*, Math. Systems Theory**3**(1969), 320-375. MR**0259881 (41:4510)****[K]**B. Kitchens,*Continuity properties of factor maps in ergodic theory*, Ph.D. thesis, Univ. of North Carolina, Chapel Hill, 1981.**[N]**M. Nasu,*Constant-to-one and onto global maps of homomorphisms between strongly connected graphs*, Ergodic Theory Dynamical Systems**3**(1983), 387-414. MR**741394 (85m:58162)****[P-T]**W. Parry and S. Tuncel,*Classification problems in ergodic theory*, London Math. Society Lecture Note Series**67**, Cambridge Univ. Press, 1982. MR**666871 (84g:28024)****[W1]**R. Williams,*Classification of subshifts of finite type*, Ann. of Math. (2)**98**(1973), 120-153. MR**0331436 (48:9769)****[W2]**-,*Classification of one-dimensional attractors*, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 341-361. MR**0266227 (42:1134)**

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

Retrieve articles in all journals with MSC: 28D05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938666-4

Article copyright:
© Copyright 1988
American Mathematical Society