Generalized probabilistic frames and Wasserstein distances.
(abstract,
pdf).
Preprint 20 pages, The preprint will likely be here by the end of September 24
(with Dongwei Chen, Colorado State. Former graduate student. )
Siegel-Veech constants for cyclic covers of generic translation surfaces.
(abstract,
pdf).
Preprint 80 pages, The preprint is also available on the ArXiv
(with David Aulicino, Aaron Calderon, Carlos Matheus and Nick Salter)
Ergodic Theory on coded shift spaces.
(abstract,
pdf,
Journal link (free access till 10/23/24)).
(with Tamara Kucherenko and Christian Wolf)
To appear in Advances in Mathematics, Vol 457, Nov. 2024, 43 pages.
On the computability of rotation sets and their entropies.
(abstract,
pdf).
(with Michael Burr and Christian Wolf)
Ergodic Theory and Dynamical Systems, Vol 40, Issue 2, Febr. 2020, pp. 367--401.
Orbit classification and asymptotic constants for d-symmetric covers.
(abstract,
pdf).
Preprint 37 pages,
a completely revised version
(of the preprint from 1/18/05).
Contemporary Mathematics, vol. 736, 2019 pp. 201--242.
On the ergodicity of foliations of Z^d covers with vanishing Lyapunov exponents and applications to periodic Eaton lens systems.
(abstract,
pdf).
(with Krzysztof Fraczek). Communications in Mathematical Physics 2018, 48 pages.
This is a second piece on Eaton Lenses that describes ergodic periodic lens-configurations
in the plane. Among other things this paper contains ideas how to replace folds, in the flat picture those are certain gaps where light rays jump, by optically equivalent Eaton lens configurations. We show a general ergodicity result for Z^d covers under the hypothesis of vanishing Lyapunov exponents.
Orbit behavior of light rays in some lattice systems
of retro-reflector lenses
(abstract,
pdf).
(with Krzysztof Fraczek). Nonlinearity, 18 pages.
This is an application of Panov planes to a retro-reflector
problem with a statistical physics flavor.
It was brought to our attention by Jens Marklof. We use a method
developed by Corinna Ulcigrai and Krzysztof Fraczek.
Hyperelliptic surfaces and folded tori
(abstract,
pdf).
(with Cris Johnson). 22 pages.
Given a hyperelliptic translation surface, we use a cover-quotient (or equivalently a twist) construction to construct strict half-translation
tori. We count those tori and provide polygonal representations. Topology and its Applications, Volume 161, Pages 73-94 (1 January 2014)
Orbit behavior on Panov planes in eigendirections of
pseudo-Anosov maps.
(abstract,
pdf).
(with Cris Johnson). March 2014. Revised preprint 18 pages.
To appear in ERA. Contains essential and motivating results, constructions and some proofs.
Adic Flows, Transversal Flows, and Horocycle Flows.
(abstract,
pdf).
(with Omri Sarig) Ergodic Theory Workshop Proceedings 2011 & 2012, pages 241-259.
Ergodic Theory and Dynamical Systems, Proceedings of the Ergodic Theory Workshop,
Walter De Gruyter, Dec. 2013.
Veech groups for holonomy free torus covers.
(abstract),
pdf).
This is a completely revised version with a new introduction,
33 journal pages.
Journal of Topology and Analysis. 4(3) Dec. 2011
Modular fibers and illumination problems.
(abstract,
pdf).
(with P. Hubert and S. Troubetzkoy) Int. Math. Res. Not.
IMRN 2008, no. 8, Art. ID rnn011, 42 pp.
Some statements differ a little from the ones in previous versions. Preprint, 10/2005, version Jan 06, 37 pages
Spaces of elliptic differentials.
(abstract,
pdf). In Contemporary Mathematics 385 (2005), 18 pages.
Enlarged and improved version, minor changes (connectedness proof).
Billiards in rectangles with barriers.
(abstract,
pdf)
(with A. Eskin and H. Masur).
Duke Math. J.118(2003), pp. 427--463
On the asymptotic quadratic growth rate of saddle connections
and periodic orbits on marked flat tori.
(abstract,
ps or pdf).
GAFA12(2002), no. 3, pp. 622--649
If you have online access to MathSciNet,
you can read reviews of my papers
here