Topological entropy of block maps
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- by Ethan M. Coven PDF
- Proc. Amer. Math. Soc. 78 (1980), 590-594 Request permission
Abstract:
We show that $h({f_\infty }) = \log 2$ where ${f_\infty }$ is the map on the space of sequences of zeros and ones induced by the block map $f({x_0}, \ldots ,{x_k}) = {x_0} + \Pi _{i = 1}^k({x_i} + {b_i})$ where $k \geqslant 2$ and the k-block ${b_1} \ldots {b_k}$ is aperiodic.References
- R. L. Adler, A. G. Konheim, and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309–319. MR 175106, DOI 10.1090/S0002-9947-1965-0175106-9
- R. L. Adler and M. H. McAndrew, The entropy of Chebyshev polynomials, Trans. Amer. Math. Soc. 121 (1966), 236–241. MR 189005, DOI 10.1090/S0002-9947-1966-0189005-0
- Rufus Bowen, Markov partitions for Axiom $\textrm {A}$ diffeomorphisms, Amer. J. Math. 92 (1970), 725–747. MR 277003, DOI 10.2307/2373370
- Rufus Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401–414. MR 274707, DOI 10.1090/S0002-9947-1971-0274707-X
- Rufus Bowen, On Axiom A diffeomorphisms, Regional Conference Series in Mathematics, No. 35, American Mathematical Society, Providence, R.I., 1978. MR 0482842
- Rufus Bowen and John Franks, The periodic points of maps of the disk and the interval, Topology 15 (1976), no. 4, 337–342. MR 431282, DOI 10.1016/0040-9383(76)90026-4
- Ethan M. Coven and G. A. Hedlund, Periods of some nonlinear shift registers, J. Combin. Theory Ser. A 27 (1979), no. 2, 186–197. MR 542528, DOI 10.1016/0097-3165(79)90045-1
- T. N. T. Goodman, Relating topological entropy and measure entropy, Bull. London Math. Soc. 3 (1971), 176–180. MR 289746, DOI 10.1112/blms/3.2.176
- G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3 (1969), 320–375. MR 259881, DOI 10.1007/BF01691062 L. Jonker and D. Rand, A lower bound for the entropy of certain maps of the unit interval, University of Warwick, preprint, 1978.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 590-594
- MSC: Primary 54H20; Secondary 54C70
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556638-1
- MathSciNet review: 556638