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DissertationZelada7-20-21.pdf (1.15 MB)

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Recurrence and Mixing Properties of Measure Preserving Systems and Combinatorial Applications

Zelada Cifuentes, Jose Rigoberto Enrique
http://orcid.org/0000-0003-2949-9872
http://rave.ohiolink.edu/etdc/view?acc_num=osu1626784438216632

Abstract Details

2021, Doctor of Philosophy, Ohio State University, Mathematics.
This dissertation deals with the fine structure of recurrence and mixing in probability measure preserving systems. In Chapter 2 we utilize sets of iterated differences in Ζ to obtain new Diophantine results dealing with odd polynomials. We then utilize this Diophantine results to obtain applications to ergodic theory and combinatorics. In particular, we obtain a new characterization of weakly mixing systems as well as a new variant of Furstenberg-Sárközy theorem. In Chapter 3 we utilize R-limits, a new notion of convergence based on the classical Ramsey theorem, to show that any strongly mixing probability measure preserving action of a countable abelian group is almost strongly mixing of all orders. We also obtain new characterizations of the notion of strong mixing for actions of countable abelian groups. In Chapter 4 we utilize Gaussian measure preserving systems to prove the existence and genericity of measure preserving transformations which exhibit both mixing and rigidity behavior along families of independent polynomials.
Vitaly Bergelson (Advisor)
Andriy Gogolyev (Committee Member)
Alexander Leibman (Committee Member)
186 p.
Mathematics
Ergodic theory; Ramsey theory; Ultrafilters; Diophantine approximations; strongly mixing systems; rigidity; generic transformations

Recommended Citations

Citations

  • Zelada Cifuentes, J. R. E. (2021). Recurrence and Mixing Properties of Measure Preserving Systems and Combinatorial Applications [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1626784438216632

    APA Style (7th edition)

  • Zelada Cifuentes, Jose Rigoberto Enrique. Recurrence and Mixing Properties of Measure Preserving Systems and Combinatorial Applications. 2021. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1626784438216632.

    MLA Style (8th edition)

  • Zelada Cifuentes, Jose Rigoberto Enrique. "Recurrence and Mixing Properties of Measure Preserving Systems and Combinatorial Applications." Doctoral dissertation, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1626784438216632

    Chicago Manual of Style (17th edition)

osu1626784438216632
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This open access ETD is published by The Ohio State University and OhioLINK.