1,153 research outputs found
Positive Entropy Invariant Measures on the Space of Lattices with Escape of Mass
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
Video Chat Application for Facebook
This project is mainly written for the facebook users. In today’s world, there are many social networking sites available. Among those social networking web sites, facebook is widely used web site. Like all other social networking web sites, Facebook also provides many features to attract more and more users. But it lacks in providing the most important feature of social networking, i.e. video chat. I explore the different options and requirements needed to build the video chat application. I have also described the integration of the application with the facebook
Effective uniqueness of Parry measure and exceptional sets in ergodic theory
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 of
exceptional sets arising from dynamics
Exceptional sets in homogeneous spaces and Hausdorff dimension
In this paper we study the dimension of a family of sets arising in open
dynamics. We use exponential mixing results for diagonalizable flows in compact
homogeneous spaces to show that the Hausdorff dimension of set of points
that lie on trajectories missing a particular open ball of radius is at
most where is a constant
independent of . Meanwhile, we also describe a general method for
computing the least cardinality of open covers of dynamical sets using volume
estimates.Comment: 10 page
Algebraic Numbers, Hyperbolicity, and Density Modulo One
We prove the density of the sets of the form modulo one,
where and are multiplicatively independent algebraic
numbers satisfying some additional assumptions. The proof is based on analysing
dynamics of higher-rank actions on compact abelean groups
Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension
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 flows on homogeneous spaces , where is any
connected semisimple Lie group of real rank 1 with finite center and
is any nonuniform lattice in . We show that this bound is sharp and apply
the methods used to establish bounds for the Hausdorff dimension of the set of
points which diverge on average.Comment: 24 page
Escape of mass and entropy for diagonal flows in real rank one situations
Let be a connected semisimple Lie group of real rank 1 with finite
center, let be a non-uniform lattice in and any diagonalizable
element in . We investigate the relation between the metric entropy of
acting on the homogeneous space and escape of mass.
Moreover, we provide bounds on the escaping mass and, as an application, we
show that the Hausdorff dimension of the set of orbits (under iteration of )
which miss a fixed open set is not full.Comment: 40 pages, 1 figur
Importance of van der Waals interactions for ab initio studies of topological insulators
We investigate the lattice and electronic structures of the bulk and surface
of the prototypical layered topological insulators BiSe and
BiTe using ab initio density functional methods, and systematically
compare the results of different methods of including van der Waals (vdW)
interactions. We show that the methods utilizing semi-empirical energy
corrections yield accurate descriptions of these materials, with the most
precise results obtained by properly accounting for the long-range tail of the
vdW interactions. The bulk lattice constants, distances between quintuple
layers and the Dirac velocity of the topological surface states (TSS) are all
in excellent agreement with experiment. In BiTe, hexagonal warping of
the energy dispersion leads to complex spin textures of the TSS at moderate
energies, while in BiSe these states remain almost perfectly helical
away from the Dirac point, showing appreciable signs of hexagonal warping at
much higher energies, above the minimum of the bulk conduction band. Our
results establish a framework for unified and systematic self-consistent first
principles calculations of topological insulators in bulk, slab and interface
geometries, and provides the necessary first step towards ab initio modeling of
topological heterostructures.Comment: 26 pages, 7 figures. This is the Accepted Manuscript version of an
article accepted for publication in Journal of Physics: Condensed Matter. IOP
Publishing Ltd is not responsible for any errors or omissions in this version
of the manuscript or any version derived from it. The Version of Record is
available online at https://dx.doi.org/10.1088/1361-648X/abbdb
Exceptional sets in homogeneous spaces and hausdorff dimension
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 points that lie on trajectories missing a particular open ball of radius r is at most dimX + C rdimX log r; where C > 0 is a constant independent of r > 0. Meanwhile, we also describe a general method for computing the least cardinality of open covers of dynamical sets using volume estimates
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