Publications

  • “Partially bounded transformations have trivial centralizers,” with Johan Gaebler, Alexander Kastner, Xiaoyu Xu, Zirui Zhou,  Proc. Amer. Math. Soc. 146 (2018), no. 12, 5113–5127.
  • “Weak mixing for infinite measure invertible transformations,” with Terrence Adams, Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics, 327–349, Lecture Notes in Math., 2213, Springer, Cham, 2018.
  • “Infinite symmetric ergodic index and related examples in infinite measure,” with Isaac Loh,  Studia Math. 243 (2018), no. 1, 101–115.
  • On conservative sequences and their application to ergodic multiplier problems,” with Madeleine Elyze; Alexander Kastner; Juan Ortiz Rhoton; Vadim Semenov, Colloq. Math. 151 (2018), no. 1, 123–145.
  • “Strict doubly ergodic infinite transformations,” with Isaac Loh,  Dyn. Syst. 32 (2017), no. 4, 519–543.
  • “On mixing-like notions in infinite measure,” Amer. Math. Monthly 124 (2017), no. 9, 807–825.
  • If a prime divides a product.,” with Steven J. Miller, College Math. J. 48 (2017), no. 2, 123–128.
  • “The mathematical work of John C. Oxtoby,” with Steve Alper, Joseph Auslander, Ergodic theory, dynamical systems, and the continuing influence of John C. Oxtoby, 43–51, Contemp. Math., 678, Amer. Math. Soc., Providence, RI, 2016.
  • “Weak Rational Ergodicity Does Not Imply Rational Ergodicity,” with Terrence M. Adams, Israel Journal of Mathematics, 2144 (2016), no. 1, 491-506.  http://arxiv.org/abs/1502.06566
  • “Ergodicity and Conservativity of products of infinite transformations and their inverses,” with Julien Clancy, Rina Friedberg, Isaac Loh, Indraneel Kalsmarka, Sahana Vasudevan, Colloq. Math. 143 (2016), no. 2, 271-291. http://arxiv.org/abs/1408.2445
  • What is an ergodic transformation?” Notices Amer. Math. Soc. 63 (2016), no. 1, 26–27.
  • “On Infinite Transformations with Maximal Control of Ergodic Two-fold Product Powers,” with Terrence M. Adams, Israel Journal of Mathematics, 209 (2015), no. 2, 929-948. http://arxiv.org/abs/1402.1818
  • “Subsequence Bounded Rational Ergodicity of Rank-One Transformations,” with Francisc Bozgan, Anthony Sanchez, David Stevens and Jane Wang, Dynamical Systems, 30 (2015), no. 1, 70–84. SubsequenceRatErgRankOne.pdf 
    For an older more extensive version: http://arxiv.org/abs/1310.5084
  • “On $v$-Positive Type Transformations in Infinite Measure,” with Tudor Padurariu and Evangelie Zachos, Colloq. Math. 140 (2015), 149—170. On $v$-Positive Type Transformations in Infinite Measure
  • “On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations,” with Irving Dai, Xavier Garcia, and Tudor Padurariu, Ergodic Theory & Dynamical Systems 35 (2015), no. 4, 1141–1164. On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations
  • “On Li-Yorke Measurable Sensitivity,” with Jared Hallett and Lucas Manuelli, Proc. Amer. Math. Soc. 143 (2015), no. 6, 2411–2426. On Li-Yorke Measurable Sensitivity
  • “Measurable Time-Restricted Sensitivity,” with Domenico Aiello, Hansheng Diao, Zhou Fan, Daniel O. King, and Jessica Lin, Nonlinearity 25 (2012), 3313–3325.Measurable Time-Restricted Sensitivity
  • “On $mu$-Compatible Metrics and Measurable Sensitivity,” with Ilya Grigoriev, Nathaniel Ince, Marius Catalin Iordan, Amos Lubin, Colloquium Math. 126 (2012), 53–72. On $mu$-Compatible Metrics 
  • “Digraph Representations of Rational Functions over $p$-adic Numbers,” with Hansheng Diao, P-adic Numbers, Ultrametric Analysis, and Applications, Vol. 3, No. 1, (2011) 23–38. Digraph Representations 
  • “Dynamics of the $p$-adic shift and Applications,” with J. Kingsbery, A. Levin, and A. Preygel, Discrete and Continuous Dynamical Systems, 30, (2011), no. 1, 209–218. Dynamics of the $p$-adic shift and Applications 
  • “Mixing on Rank-One Transformations,” with D. Creutz, Studia Math. 199 (2010), no. 1, 43–72. MixingRankOne.pdf 
  • “Ergodic Properties of a Class of Discrete Abelian Group Extensions of Rank-One Transformations,” P. Jeasakul, A. Jirapattanakul, D. Kane, B. Robinson, and N. Stein, Colloq. Math., 119 (2010), 1-22. Small04May_5_2009.pdf 
  • “On ergodic transformations that are both weakly mixing and uniformly rigid,” with J. James, T. Koberda, K. Lindsey, and P. Speh, New York Journal of Math. 15 (2009), 393–403. Weakly mixing and uniformly rigid 
  • “Ergodic Theory: Nonsingular Transformations,” with A. Danilenko, Encyclopedia of Complexity and Systems Science, Springer, (2009), Part 5, 3055-3083.NonsingularTransformations.pdf 
  • “Measurable Sensitivity,” with J. James, T. Koberda, K. Lindsey, and P. Speh, Proc. Amer. Math. Soc. 136 (2008), no. 10, 3549–3559. MeasurableSensitivity 
  • “Measurable Dynamics of Maps on Profinite Groups,” with J. Kingsbery, A. Levin, and A. Preygel, Indag. Math. (N.S.) 18 (2007), no. 4, 561–581. ProfiniteGroups.pdf 
  • “On measure-preserving C^1 transformations of compact-open subsets of non-archimedean local fields,” with J. Kingsbery, A. Levin, and A. Preygel, Tran. Amer Math. Soc. 361 (2009), 61-85. Early version: LocallyScaling.pdf 
  • “Mixing rank-one actions of locally compact abelian groups,” with A. Danilenko, Ann. Inst. H. Poincaré Probab. Statist. 43 (2007), no. 4, 375–398.MixingAbelianGroups.pdf 
  • “Weakly Mixing and Doubly Ergodic Infinite Measure-Preserving R^d actions,” with S. Iams, B. Katz, B. Street, and K. Wickelgren, Colloq. Math. 103 (2005), 247-264. WeaklyMixingRd.pdf 
  • “Measurable Dynamics of Simple p-adic Polynomials,” with J. Bryk, Amer. Math. Monthly, Vol. 112 (2005), no. 3, 212-232. pAdicMeasurableSystems.pdf 
  • “Multiple and Polynomial Recurrence for Abelian Actions in Infinite Measure,” with A. Danilenko, Journal London Math. Soc. (2) 69 (2004), no. 1, 183-200. AbelianMultRec.pdf 
  • “Power Weak Mixing does not imply Multiple Recurrence in Infinite Measure and other Counterexamples,” with K. Gruher, F. Hines, D. Patel, and R. Waelder, New York Journal of Mathematics 9 (2003), 1-22.http://nyjm.albany.edu:8000/j/2003/Vol9.htm 
  • “Mixing on a class of rank one transformations,” with D. Creutz, Ergodic Theory and Dynam. Sys. 24 (2004), no. 2, 407-440. RankOneMixingClass.pdf
  • “Genericity of Rigid and Multiply Recurrent Infinite Measure Preserving and Nonsingular Transformations,” with O. N. Ageev, Topology Proceedings 26 No. 2 (2001-2002), pp. 357-365. GenMultRec.pdf
  • “Double Ergodicity of Nonsingular Transformations and Infinite Measure Preserving Staircase Transformations,” with A. Bowels, L. Fidkowski, and A.E. Marinello, Illinois J. Math., Vol. 45, No. 3, (2001), 999-1019.
  • “Factors of Cartesian products of nonsingular Chacon transformations,” with A. del Junco, Ergodic Theory and Dynam. Sys. 23 (2003), 1445-1465. FactorsTxS.pdf
  • “On nonsingular Chacon transformations,” with T. Hamachi, Illinois J. Math., Vol. 44, No. 4, (2000), 868-883.
  • “Rank one power weakly mixing nonsingular transformations,” with T. Adams and N. Friedman, Ergodic Theory and Dyn. Sys. 21 (2001), no. 5, 1321–1332.
  • “Power weakly mixing infinite transformations,” with S.L. Day, B.R. Grivna, and E.P. McCartney, New York J. of Math., 5 (1999), 17-24. http://nyjm.albany.edu:8000/j/1999/5-2.html
  • “Lightly mixing on dense algebras,” with E. Muehlegger, A. Raich, and W. Zhao, Real Analysis Exchange, Vol. 23, No. 1, (1998), 259-266. [MR 99c:28052].
  • “Zd staircase actions,” with T. Adams, Ergodic Theory and Dyn. Sys., (1999), 19, 837-850. May be downloaded from http://www.journals.cup.org/
  • “Infinite ergodic index Zd actions in infinite measure,” with E. Muehlegger ’97, B. Narasimhan ’97, A. Raich ’98, M.Touloumtzis ‘ 96, and W. Zhao, Colloq. Math., vol. 82, No. 2 (1999), 167-190.
  • “Characterizing mildly mixing group actions using orbit equivalence,” with J. Hawkins, New York J. of Math., 3A (1998), 99-115. [MR 99b:28019]. http://nyjm.albany.edu:8000/j/1998/3A-8.html
  • “Rank-one weak-mixing for nonsingular transformations,” with T. Adams and N. Friedman, Israel J. Math, vol. 102, (1997), 269-282. [MR 98j:28013].
  • “Prime type IIIl automorphisms: An instance of coding techniques applied to nonsingular maps,” with A. del Junco, in Algorithms, Fractals and Dynamics (Okayama/Kyoto, 1992), 101-115, Plenum, New York, 1995. [MR 98f:28026].
  • “Quotients of ergodic actions with quasi-invariant measure whose self-joinings are graphs,” with D. Witte, Inter. J. Math. 5 (2) (1994), 219-237. [MR: 95k:28042].
  • “A skew product entropy for nonsingular transformations,” with P. Thieullen, J. London Math. Soc. (2) 52 (1995), 497-516. [MR 97a: 28015].
  • “Noninvertible transformations admitting no absolutely continuous s-finite invariant measure,” with J.M Hawkins, Proc. Amer. Math. Soc. 111 (2) (1991), 455-463. [MR 92h:58115].
  • “Minimal self-joinings for nonsingular transformations,” with D.J. Rudolph, Ergodic Theory and Dyn. Sys. 9 (1989), 759-800. [MR 91c: 28017].
  • “The subadditive ergodic theorem and recurrence properties of Markovian transformations,” with P. Thieullen, J. Math. Analysis and App. 154 (1) (1991), 83-99. [MR 92a: 47009].
  • “Finite Full Sets in 2-stack Structures,” with S. Eigen, Contemporary Math. 94 (1989), 131-140. [MR 90h: 28018].
  • “Remarks on recurrence and orbit equivalence of nonsingular transformations,” with J. Hawkins, Dynamical Systems (College Park, MD, 1986-87), 281-290, Lecture Notes in Math., 1342, Springer, Berlin-New York, 1988. [MR 90i: 28031].
  • “A structure theorem for n-to-1 nonsingular endomorphisms and existence of non-recurrent measures,” with S. Eigen, J. London Math. Soc. (2) 40 (1989), 441-451. [MR 91e:28013].
  • “On µ-recurrent nonsingular endomorphisms,” Israel J. Math. 61 (1988), 1-13. [MR 89f:28042].
  • “Truncated ergodic theorems for nonsingular transformations,” Rocky Mountain J. Math. 20 (1) (1990), 223-241. [Mathematical Reviews 91f:28011].