k-fold mixing lifts to weakly mixing isometric extensions

Daniel J. Rudolph

doi:10.1017/S0143385700003060

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If is a weakly mixing isometric extension of a finite measure preserving, k-fold mixing map T, then must also be k-fold mixing.

References

REFERENCES

[1]Parry, W.. Ergodic properties of affine transformations and flows on nilmanifolds. Amer. J. of Math. 91 (1969), 757–771.CrossRef Google Scholar

[2]Rudolph, D.. Classifying the isometric extensions of a Bernoulli shift. J. d'Analyse Math. 34 (1978), 36–60.CrossRef Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Rudolph, Daniel J. 1986. ℤn and ℝn cocycle extensions and complementary algebras. Ergodic Theory and Dynamical Systems, Vol. 6, Issue. 4, p. 583.

Robinson, E. Arthur 1988. Ergodic properties that lift to compact group extensions. Proceedings of the American Mathematical Society, Vol. 102, Issue. 1, p. 61.

Robinson, E. Arthur 1992. The maximal abelian subextension determines weak mixing for group extensions. Proceedings of the American Mathematical Society, Vol. 114, Issue. 2, p. 443.

Robinson, E. Arthur 1992. A general condition for lifting theorems. Transactions of the American Mathematical Society, Vol. 330, Issue. 2, p. 725.

Flaminio, L. 1993. Mixing 𝑘-fold independent processes of zero entropy. Proceedings of the American Mathematical Society, Vol. 118, Issue. 4, p. 1263.

Siboni, S 1994. Ergodic properties of a class of skew-systems obtained by coupling the translation of the 1-torus with the endomorphism 2x mod (0,1(. Nonlinearity, Vol. 7, Issue. 4, p. 1133.

Ryzhikov, V. V. 1996. Stochastic intertwinings and multiple mixing of dynamical systems. Journal of Dynamical and Control Systems, Vol. 2, Issue. 1, p. 1.

Siboni, S. 1997. Statistical properties of skew-endomorphisms with Bernoulli base. Physica D: Nonlinear Phenomena, Vol. 99, Issue. 4, p. 407.

Lemańczyk, Mariusz and Lesigne, Emmanuel 2001. Ergodicity of Rokhlin cocycles. Journal d'Analyse Mathématique, Vol. 85, Issue. 1, p. 43.

Lemańczyk, Mariusz 2009. Encyclopedia of Complexity and Systems Science. p. 8554.

Lemańczyk, Mariusz 2012. Mathematics of Complexity and Dynamical Systems. p. 1618.

DANILENKO, ALEXANDRE I. 2012. New spectral multiplicities for mixing transformations. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 2, p. 517.

RUDOLPH, DANIEL J. 2012. Informal research statement. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 2, p. 323.

LEMAŃCZYK, MARIUSZ and PARREAU, FRANÇOIS 2012. Lifting mixing properties by Rokhlin cocycles. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 2, p. 763.

DANILENKO, ALEXANDRE I. 2013. A survey on spectral multiplicities of ergodic actions. Ergodic Theory and Dynamical Systems, Vol. 33, Issue. 1, p. 81.

Dirbák, Matúš 2015. Minimal extensions of flows with amenable acting groups. Israel Journal of Mathematics, Vol. 207, Issue. 2, p. 581.

Kanigowski, Adam and Lemańczyk, Mariusz 2020. Encyclopedia of Complexity and Systems Science. p. 1.

Glasner, E. Thouvenot, J.-P. and Weiss, B. 2022. On some generic classes of ergodic measure preserving transformations. Transactions of the Moscow Mathematical Society, Vol. 82, Issue. 0, p. 15.

Kanigowski, Adam and Lemańczyk, Mariusz 2023. Ergodic Theory. p. 109.

AUSTIN, TIM GLASNER, ELI THOUVENOT, JEAN-PAUL and WEISS, BENJAMIN 2023. An ergodic system is dominant exactly when it has positive entropy. Ergodic Theory and Dynamical Systems, Vol. 43, Issue. 10, p. 3216.

Article contents

k-fold mixing lifts to weakly mixing isometric extensions

Abstract

References

REFERENCES

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests