Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Graphic flows and multiple disjointness


Authors: Joseph Auslander and Nelson Markley
Journal: Trans. Amer. Math. Soc. 292 (1985), 483-499
MSC: Primary 54H20; Secondary 28D05
DOI: https://doi.org/10.1090/S0002-9947-1985-0808733-6
MathSciNet review: 808733
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A graphic flow is a totally minimal flow for which the only minimal subsets of the product flow are the graphs of the powers of the generating homeomorphism. The POD flows of Furstenberg, Keynes, and Shapiro [5] are examples of graphic flows. Graphic flows are in some ways analogous to ergodic systems with minimal self-joinings [11]. Various disjointness results concerning graphic flows and their powers are obtained, and their regular factors are determined.


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

  • [1] J. Auslander, Regular miminal sets. I, Trans. Amer. Math. Soc. 123 (1966), 469-479. MR 0193629 (33:1845)
  • [2] R. Chacon, Weakly mixing transformations which are not strongly mixing, Proc. Amer. Math. Soc. 22 (1969), 559-562. MR 0247028 (40:297)
  • [3] J. P. Clay, Proximity relations in transformation groups, Trans. Amer. Math. Soc. 108 (1963), 88-96. MR 0154269 (27:4218)
  • [4] R. Ellis, Lectures on topological dynamics, Benjamin, New York, 1969. MR 0267561 (42:2463)
  • [5] H. Furstenberg, H. Keynes and L. Shapiro, Prime flows in topological dynamics, Israel J. Math. 14 (1973), 26-38. MR 0321055 (47:9588)
  • [6] S. Glasner, Proximal flows, Lecture Notes in Math., vol. 517, Springer-Verlag, 1976. MR 0474243 (57:13890)
  • [7] A. del Junco, A family of counterexamples in ergodic theory, preprint. MR 896794 (88k:54061)
  • [8] H. Keynes, The structure of weakly mixing minimal transformation groups, Illinois J. Math. 15 (1971), 475-489. MR 0286090 (44:3306)
  • [9] H. Keynes and D. Newton, Real prime flows, Trans. Amer. Math. Soc. 217 (1976), 237-255. MR 0400189 (53:4024)
  • [10] N. Markley, Toplogical minimal self-joinings, Ergodic Theory and Dynamical Systems 3 (1983), 579-599. MR 753925 (85h:54078)
  • [11] D. Rudolph, An example of a measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122. MR 555301 (81e:28011)
  • [12] T. Wu, Notes on topological dynamics. II. Distal extension with discrete fibers and prime flows, Bull. Inst. Math. Acad. Sinica 3 (1975), 49-60. MR 0405388 (53:9182)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54H20, 28D05

Retrieve articles in all journals with MSC: 54H20, 28D05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0808733-6
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society