Analytic Self-Maps of Cantor Sets in the Line
preprint.
A short proof of Host's equidistribution theorem
Israel Journal of Mathematics 2013, vol 251, 527-539, journal, arxiv
Hausdorff dimension of planar self-affine sets and measures with overlaps
With Ariel Rapaport.
Journal of the EMS 2022, Vol 24, No. 7, pp. 2361-2441,journal, arxiv
Hausdorff dimension of planar self-affine sets and measures
With Baláz Bárány and Ariel Rapaport.
Inventiones Mathematicae 2019 Volume 216, Issue 3, pp 601–659, journal, arxiv
Smooth symmetries of xa invariant sets
Journal of Modern Dynamics, 2018, vol 13, pp 187-197. journal, arxiv.
Dimension theory of self-similar sets and measures
Proceedings of the ICM 2018. pdf
On the dimension of Furstenberg measure for SL(2,R) random matrix products
With Boris Solomyak.
Inventiones Mathematicae 2017, Volume 210, Issue 3, pp 815–875, journal, arxiv.
.
Some problems on the boundary of fractal geometry and additive combinatorics
Recent Developments in Fractals and Related Fields, 2017, pp 129-174, journal, arxiv.
Self embeddings of Bedford-McMullen carpets
With Amir Algom.
To appear in Ergodic Theory Dynamical Systems, journal, arxiv.
On self-similar sets with overlaps and inverse theorems for entropy in R^d
To appear in Memoires of the AMS, preprint, arxiv.
Equidistribution from fractal measures
With Pablo Shmerkin.
Inventiones Mathematicae Volume 202 (2015), Issue 1, pp 427-479, journal,
arxiv.
Self-similar sets, entropy and additive combinatorics
In Geometry and Analysis of Fractals,
Springer Proceedings in Mathematics & Statistics Volume 88, 2014, pp 225-252,
book,
arxiv,
Remark about print version.
On self-similar sets with overlaps and inverse theorems for entropy
Annals of Mathematics 180 (2014), no. 2, 773–822.
journal,
arxiv.
Geometric rigidity of times-m invariant measures
Journal of the European Mathematical Society, Volume 14, Issue 5, 2012, pp. 1539–1563,
journal,
arxiv,
erratum.
Local entropy averages and projections of fractal measures.
With Pablo Shmerkin.
Annals of Mathematics, Volume 175 Number 3 (2012), 1001-1059,
journal,
arxiv.
Lectures on dynamics, fractal geometry and metric number theory.
Lecture notes from the 2011 Bedlewo summer schoold on “Modern Dynamics and
its Interaction with Analysis, Geometry and Number Theory”. The notes cover Fursteneb
rg's theory of CP chains, and applications to intersections and projections of fracta
ls (including Furstenberg's 1970 theorem on intersections of Cantor sets and the Pere
s-Shmerkin and Hochman-Shmerkin theorems on projections. pdf, journal version.
Probability measures on R^d are amenable
This unpublished note is the measure-theoretic analogue of the main lemma in my paper on ratio ergodic theorems.
It is apparently not known (let me know if you have seen it before). pdf
Some remarks about self-products and entropy
arxiv
A short proof of Host's equidistribution theorem
Israel Journal of Mathematics 2022, vol 251, 527-539, joural, arxiv
Every Borel automorphism without finite invariant measures admi\
ts a two-set generator
Journal of the European Mathematical Society, Volume 21, Issue 1, 201\
9, pp. 271–317, journal, arxiv.
On the finite-dimensional marginals of shift-invariant measures
With
J.-R. Chazottes , J.-M. Gambaudo , and E.
Ugalde .
Ergodic Theory and Dynamical Systems, Volume 32, Issue 5, 2012 , pp 1485-1500, journal, arxiv
On zero-temperature limits of Gibbs states.
With J.R. Chazottes,
Communications in Mathematical Physics Volume 297, Number 1 / July, 2010, 265-281.
journal,
arxiv,
Clarification.
Upcrossing inequalities for stationary sequences and applications to entropy and complexity
Ann. Probab. Volume 37, Number 6 (2009), 2135-2149.
journal,
arxiv.
On processes which cannot be distinguished by finitary observation.
With Yonatan Gutman,
Israel journal of Mathematics, Volume 164, Number 1 / March, 2008,
journal,
arxiv.
Return times, recurrence densities and entropy for actions of some discrete amenable groups,
Journal d'Analyse Mathematique, Volume 100, Number 1 / December, 2006,
journal,
arxiv.<
Recurrence densities -- short version
This unbulished note is a short (6 pages, incl. intro & bib) version of the main result from the paper above, formulated for stationary processes (indexed by Z rather than a general amenable group).pdf
On one-sided and two sided ergodic averages of non-integrable functions.
This unpublished note answers a question raised by Yves Derriennic in the Fall 2008 semester on Ergodic Theory at MSRI. In retrospect it is a pretty simple thing. A similar proof was given independently by Benjamin Weiss. pdf.
Every Borel automorphism without finite invariant measures admits a two-set generator
Journal of the European Mathematical Society, Volume 21, Issue 1, 2019, pp. 271-317, journal, arxiv.
On the ratio ergodic theorem for group actions
Journal of the London Mathematical Society (2) 88 (2013), no. 2, 465–482 journal, arxiv.
Slow entropy and differentiable models for infinite measure preserving Z^d actions
Ergodic Theory and Dynamical Systems 32 (2012), 653--674 (special volume in memory of Dan Rudolph),
journal,
arxiv.
A ratio ergodic theorem for multiparameter actions.
Journal of the European Mathematical Society 12 (2010), no. 2, 365--383.
journal,
arxiv.
Irreducibility and Periodicity in Z^2 Symbolic Systems
arxiv.
On the Turing Degree Spectra of Minimal Subshifts
With Pascal Vanier.
CSR 2017, pp 154-161, journal, arxiv.
Isomorphism and embedding into Markov shifts off universally null sets
Acta Applicandae Mathematicae: Volume 126 (Hang Kim Memorial Volume), Issue 1 (2013), Page 187-201.
journal,
arxiv,
erratum.
On the finite-dimensional marginals of shift-invariant measures
With
J.-R. Chazottes , J.-M. Gambaudo , and E.
Ugalde .
Ergodic Theory and Dynamical Systems, Volume 32, Issue 5, 2012 , pp 1485-1500, journal, arxiv
Inverses, products and cartesian powers of topologically
deterministic maps
With Artur Siemaszko
Topological Methods in Nonlinear Analysis 39 (2012) No. 1,
journal,
arxiv.
Rohlin properties for $Z^d$-actions on the Cantor set.
Transactions of the AMS 364 (2012) No. 3, 1127--1143,
journal,
arxiv.
On notions of determinism in topological dynamics.
Ergodic Theory Dynamical Systems, 32 (2012) no. 1, 119--140,
journal,
arxiv.
Non-expansive directions for $Z^2$ actions.
Ergodic Theory Dynamical Systems 31 (2011), no. 1, 91--112,
journal,
arxiv.
A Characterization of the Entropies of Multidimensional Shifts of Finite Type.
With Tom Meyerovitch,
Annals of Mathematics Vol. 171 (2010), No. 3, 2011-2038,
Journal,
arxiv.
On the automorphism group of multidimensional SFTs.
Ergodic Theory Dynamical Systems (2010), 30, 809--840.
journal,
preprint.
On universality in multidimensional symbolic dynamics,
Discrete and Continuous Dynamical Systems S, Volume: 2, No. 2, 2009.
arxiv,
journal.
On the dynamics and recursive properties of multidimensional symbolic systems .
Inventiones Mathematica, Volume 176, Number 1, April, 2009.
journal,
preprint.
Genericity in Topological Dynamics.
Ergodic Theory Dynamical Systems (2008), 28 : 125-165,
journal
arxiv..
Examples of non-polygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
With Michael Damron.
Annals of Applied Probability 2013, Vol. 23, No. 3, 1074-1085, journal,
arxiv.
Upcrossing inequalities for stationary sequences and applications to entropy and complexity
Ann. Probab. Volume 37, Number 6 (2009), 2135-2149.
journal,
arxiv.
On processes which cannot be distinguished by finitary observation.
With Yonatan Gutman,
Israel journal of Mathematics, Volume 164, Number 1 / March, 2008,
journal,
arxiv.
Averaging sequences and abelian rank in amenable groups.
Israel Journal of Mathematics, Volume 158, Number 1 / March, 2007,
journal,
arxiv..
Together with my friends Yonatan Harel, Ittay Weiss and Ofek Shilon, I have written a calculus textbook to accompany the first year course given at the Hebrew University (the book is in Hebrew, of course). Here is the table of contents. The book is available from Academon Press. Corrections can be found on the book site.