Volume 2 (2019)
Janvresse, Élise; Roy, Emmanuel; de la Rue, Thierry
Nearly finite Chacon transformation
Annales Henri Lebesgue, Volume 2 (2019), pp. 369-414.

Metadata

DOI10.5802/ahl.21
Keywords Chacon infinite measure preserving transformation, rank-one transformation, joinings.

Abstract

We construct an infinite measure preserving version of Chacon transformation, and prove that it has a property similar to Minimal Self-Joinings in finite measure: its Cartesian powers have as few invariant Radon measures as possible.


References

[Aar97] Aaronson, Jon An introduction to infinite ergodic theory, Mathematical Surveys and Monographs, 50, American Mathematical Society, 1997, xii+284 pages | MR | Zbl

[AFS97] Adams, Terrence; Friedman, Nathaniel; Silva, Cesar E. Rank-one weak mixing for nonsingular transformations, Isr. J. Math., Volume 102 (1997), pp. 269-281 | DOI | MR | Zbl

[BSS + 15] Bozgan, Francisc; Sanchez, Anthony; Silva, Cesar E.; Stevens, David; Wang, Jane Subsequence bounded rational ergodicity of rank-one transformations, Dyn. Syst., Volume 30 (2015) no. 1, pp. 70-84 | DOI | MR | Zbl

[Dan18] Danilenko, Alexandre I. Infinite measure preserving transformations with Radon MSJ., Isr. J. Math., Volume 228 (2018) no. 1, pp. 21-51 | DOI | MR | Zbl

[dJRS80] del Junco, Andres; Rahe, Maurice; Swanson, Laif Chacon’s automorphism has minimal self-joinings, J. Anal. Math., Volume 37 (1980), pp. 276-284 | DOI | MR | Zbl

[FS67] Foias, Ciprian; Stratila, Serban Ensembles de Kronecker dans la Théorie ergodique, C. R. Math. Acad. Sci. Paris, Volume 267 (1967), pp. 166-168 | Zbl

[Hal50] Halmos, Paul R. Measure Theory, D. Van Nostrand Company, 1950, xi+304 pages | Zbl

[JRdlR17] Janvresse, Élise; Roy, Emmanuel; de la Rue, Thierry Poisson suspensions and SuShis, Ann. Sci. Éc. Norm. Supér., Volume 50 (2017) no. 6, pp. 1301-1334 | DOI | MR | Zbl

[JRdlR18] Janvresse, Élise; Roy, Emmanuel; de la Rue, Thierry Invariant measures for Cartesian powers of Chacon infinite transformation, Isr. J. Math., Volume 224 (2018), pp. 1-37 | DOI | MR | Zbl

[LPT00] Lemańczyk, Mariusz; Parreau, François; Thouvenot, Jean-Paul Gaussian automorphisms whose ergodic self-joinings are Gaussian, Fundam. Math., Volume 164 (2000) no. 3, pp. 253-293 | MR | Zbl

[Roy07] Roy, Emmanuel Ergodic properties of Poissonian ID processes, Ann. Probab., Volume 35 (2007) no. 2, pp. 551-576 | MR | Zbl

[Rud79] Rudolph, Daniel J. An example of a measure preserving map with minimal self-joinings, and applications, J. Anal. Math., Volume 35 (1979), pp. 97-122 | DOI | MR | Zbl