Zobrazeno 1 - 10
of 129
pro vyhledávání: '"Eskin, Alex"'
We revisit the theory of normal forms for non-uniformly contracting dynamics. We collect a number of lemmas and reformulations of the standard theory that will be used in other projects.
Externí odkaz:
http://arxiv.org/abs/2405.16208
We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any compactly
Externí odkaz:
http://arxiv.org/abs/2305.06009
We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order templates for the
Externí odkaz:
http://arxiv.org/abs/2302.12981
We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing
Externí odkaz:
http://arxiv.org/abs/1905.04435
Autor:
Chaika, Jon, Eskin, Alex
We show that typical interval exchange transformations on three intervals are not 2-simple answering a question of Veech. Moreover, the set of self-joinings of almost every 3-IET is a Paulsen simplex.
Comment: 25 pages, 3 figures
Comment: 25 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/1805.11167
We consider the action of $SL(2,\mathbb{R})$ on a vector bundle $\mathbf{H}$ preserving an ergodic probability measure $\nu$ on the base $X$. Under an irreducibility assumption on this action, we prove that if $\hat\nu$ is any lift of $\nu$ to a prob
Externí odkaz:
http://arxiv.org/abs/1709.02521
We compute the algebraic hull of the Kontsevich-Zorich cocycle over any GL^+_2(R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.
Externí odkaz:
http://arxiv.org/abs/1702.02074
Publikováno v:
Geometry and Topology, 22:4 (2018), 2299-2338
Consider a flat bundle over a complex curve. We prove a conjecture of Fei Yu that the sum of the top k Lyapunov exponents of the flat bundle is always greater or equal to the degree of any rank k holomorphic subbundle. We generalize the original cont
Externí odkaz:
http://arxiv.org/abs/1609.01170
Autor:
Chaika, Jon, Eskin, Alex
We show that Sarnak's conjecture on Mobius disjointness holds for interval exchange transformations on three intervals (3-IETs) that satisfy a mild diophantine condition.
Comment: 32 pages, 3 figures
Comment: 32 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/1606.02357
Autor:
Eskin, Alex, Zorich, Anton
Publikováno v:
Arnold Mathematical Journal, 1:4 (2015) 481-488
We state conjectures on the asymptotic behavior of the volumes of moduli spaces of Abelian differentials and their Siegel-Veech constants as genus tends to infinity. We provide certain numerical evidence, describe recent advances and the state of the
Externí odkaz:
http://arxiv.org/abs/1507.05296