We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices
It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension ...
Let G be a connected semisimple Lie group of real rank 1 with finite center, let be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting ...
Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal
ows on homogeneous spaces nG, where G is any connected ...
In this paper we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable ows in compact homogeneous spaces X to show that the Hausdorff dimension of set of ...
Let x = (x1; : : : ; xd) 2 [1; 1]d be linearly independent over Z, set K = f(ez; ex1z; ex2z : : : ; exdz) : jzj 1g:We prove sharp estimates for the growth of a polynomial of degree n, in terms of En(x) := supfkPk d+1 ...
Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a su cient condition on a, so that for every 1 a {computable family of two embedded sets, i.e. two sets A;B, with A properly contined in B, ...
We give a su cient condition for an in nite computable family of 1
a sets, to have computable positive but undecidable numberings, where a
is a notation for a nonzero computable ordinal. This extends a theorem
proved ...
We show that for every n 1, there exists a 1n -computable family which up to equivalence has exactly one Friedberg numbering which does not induce the least element of the corresponding Rogers semilattice.
Singular systems of linear forms were introduced by Khintchine
in the 1920s, and it was shown by Dani in the 1980s that they
are in one-to-one correspondence with certain divergent orbits of oneparameter
diagonal groups ...
On the space of unimodular lattices, we construct a sequence of
invariant probability measures under a singular diagonal element with high
entropy and show that the limit measure is 0