Informal research statement

Cites Work

$T,T^{-1}$ transformation is not loosely Bernoulli
If a two-point extension of a Bernoulli shift has an ergodic square, then it is Bernoulli
If a finite extension of a Bernoulli shift has no finite rotation factors, it is Bernoulli
Classifying the isometric extensions of a Bernoulli shift
The conjugacy problem in ergodic theory
Absolutely continuous cocycles over irrational rotations
A dyadic endomorphism which is Bernoulli but not standard
Conditional entropy theory in infinite measure and a question of Krengel
Measured topological orbit and Kakutani equivalence
An isomorphism theory for Bernoulli free Z-skew-compact group actions
On the conjugacy relation in ergodic theory
Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
Any two irreducible Markov chains of equal entropy are finitarily Kakutani equivalent
Any two irrational rotations are nearly continuously Kakutani equivalent
Entropy and isomorphism theorems for actions of amenable groups
Asymptotically Brownian skew products give non-loosely Bernoulli K- automorphisms
An example of a measure preserving map with minimal self-joinings, and applications
Sizes of order statistical events of stationary processes
A two-valued step coding for ergodic flows
Two nonisomorphic K-automorphisms with isomorphic squares
The limit set of a Fuchsian group
Two nonisomorphic K-automorphisms all of whose powers beyond one are isomorphic
The limits in $d$ of multi-step Markov chains
On attaining d
The second centralizer of a Bernoulli shift is just its powers
Counting the relatively finite factors of a Bernoulli shift
Bernoulli schemes of the same entropy are finitarily isomorphic
Bernoullis are standard when entropy is not an obstruction
A class of real cocycles having an analytic coboundary modification
Fully generic sequences and a multiple-term return-times theorem
Entropy and mixing for amenable group actions
Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers
Simple systems and their higher order self-joinings
Weak isomorphism of measure-preserving diffeomorphisms
Uniform endomorphisms which are isomorphic to a Bernoulli shift
Rational maps are $d$-adic Bernoulli
The spectrum of completely positive entropy actions of countable amenable groups
Almost block independence and Bernoullicity of $\mathbb{Z}^ d$-actions by automorphisms of compact Abelian groups
Wiener-Wintner return-times ergodic theorem
Convergence under $\times_q$ of $\times_p$ invariant measures on the circle
Residual behavior of induced maps
Nearly continuous Kakutani equivalence of adding machines
Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
Bernoulli shifts with the same entropy are isomorphic
An entropy-preserving Dye's theorem for ergodic actions
Any two irreducible Markov chains are finitarily orbit equivalent
ℤⁿ and ℝⁿ cocycle extensions and complementary algebras
Commuting endomorphisms of the circle
Uncountably many topological models for ergodic transformations
Inner and barely linear time changes of ergodic 𝑅^{𝑘} actions
On Groups of Measure Preserving Transformations. I
Stability of m-equivalence to the weak Pinsker property
×2 and ×3 invariant measures and entropy
Continuity of conditional measures associated to measure-preserving semiflows
A mixing Markov chain with exponentially decaying return times is finitarily Bernoulli
k-fold mixing lifts to weakly mixing isometric extensions
Dynamical systems with hyperbolic structure
Loose Bernoullicity is preserved under exponentiation by integrable functions
Minimal self-joinings for nonsingular transformations
An ergodic transformation with trivial Kakutani centralizer
${\bi T},{\bi T}^{\bf -1}$ is not standard
Tiling representations of ${\Bbb R}^{\bf 2}$ actions and $\balpha$-equivalence in two dimensions
α-equivalence: a refinement of Kakutani equivalence
A joinings proof of Bourgain's return time theorem
Restricted orbit equivalence for ergodic ${\Bbb Z}^{d}$ actions I
Topological weak-mixing of interval exchange maps
If the [T, Id automorphism is Bernoulli then the [T, Id] endomorphism is standard]
Entropy pairs for a measure
Ergodic transformations conjugate to their inverses by involutions
Flow–orbit equivalence for minimal Cantor systems
The Morse minimal system is finitarily Kakutani equivalent to the binary odometer
Non-Bernoulli systems with completely positive entropy
FINITARY ORBIT EQUIVALENCE OF ODOMETERS
Quasi-Flows
Entropy and dyadic equivalence of random walks on a random scenery

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