Periodic points for homeomorphisms of hereditarily decomposable chainable continua
Author:
W. T. Ingram
Journal:
Proc. Amer. Math. Soc. 107 (1989), 549-553
MSC:
Primary 54F20
DOI:
https://doi.org/10.1090/S0002-9939-1989-0984796-1
MathSciNet review:
984796
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper it is shown that homeomorphisms of hereditarily decomposable chainable continua cannot have periodic points whose periods are not powers of two. Examples show that for each power of two there is a hereditarily decomposable chainable continuum and a homeomorphism of it which has a periodic point of period that power of two.
- [1] R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653–663. MR 43450
- [2] W. T. Ingram, Concerning periodic points in mappings of continua, Proc. Amer. Math. Soc. 104 (1988), no. 2, 643–649. MR 962842, https://doi.org/10.1090/S0002-9939-1988-0962842-8
- [3] D. P. Kuykendall, Irreducibility and indecomposability in inverse limits, Fund. Math. 80 (1973), no. 3, 265–270. MR 326684, https://doi.org/10.4064/fm-80-3-265-270
- [4] P. Mine and W. R. R. Transue, Sarkovskii's Theorem for hereditarily decomposable chainable continua, preprint.
- [5] Michel Smith and Sam W. Young, Periodic homeomorphisms on 𝑇-like continua, Fund. Math. 104 (1979), no. 3, 221–224. MR 559176, https://doi.org/10.4064/fm-104-3-221-224
- [6] R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), 439–460. MR 10968, https://doi.org/10.2307/2371908
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F20
Retrieve articles in all journals with MSC: 54F20
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1989-0984796-1
Keywords:
Periodic point,
atriodic,
unicoherent,
chainable continuum,
indecomposable continuum,
inverse limit
Article copyright:
© Copyright 1989
American Mathematical Society