A note on the ergodic properties of homeomorphisms
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- by Robert Sine
- Proc. Amer. Math. Soc. 57 (1976), 169-172
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402706-3
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Abstract:
Powers of strongly ergodic transformations need not be strongly ergodic.References
- Felix E. Browder, On the iteration of transformations in noncompact minimal dynamical systems, Proc. Amer. Math. Soc. 9 (1958), 773–780. MR 96975, DOI 10.1090/S0002-9939-1958-0096975-9
- Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561
- H. Furstenberg, Strict ergodicity and transformation of the torus, Amer. J. Math. 83 (1961), 573–601. MR 133429, DOI 10.2307/2372899
- Frank Hahn and William Parry, Some characteristic properties of dynamical systems with quasi-discrete spectra, Math. Systems Theory 2 (1968), 179–190. MR 230877, DOI 10.1007/BF01692514
- Benton Jamison and Robert Sine, Irreducible almost periodic Markov operators, J. Math. Mech. 18 (1968/1969), 1043–1057. MR 0242257
- G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190. MR 27868, DOI 10.1007/BF02393648
- John C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116–136. MR 47262, DOI 10.1090/S0002-9904-1952-09580-X
- Robert Sine, Geometric theory of a single Markov operator, Pacific J. Math. 27 (1968), 155–166. MR 240281
- Robert Sine, A mean ergodic theorem, Proc. Amer. Math. Soc. 24 (1970), 438–439. MR 252605, DOI 10.1090/S0002-9939-1970-0252605-X
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 169-172
- MSC: Primary 54H20; Secondary 60J05, 28A65
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402706-3
- MathSciNet review: 0402706