1,659 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
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
Unitary correlation in nuclear reaction theory
We prove that the amplitudes for the (d,p), (d,pn) and (e,e'p) reactions
determining the asymptotic behavior of the exact scattering wave functions in
the corresponding channels are invariant under unitary correlation operators
while the spectroscopic factors are not. Moreover, the exact reaction
amplitudes are not parametrized in terms of the spectroscopic factors and
cannot provide a tool to determine the spectroscopic factors.Comment: 5 page
Ship Detection and Segmentation using Image Correlation
There have been intensive research interests in ship detection and
segmentation due to high demands on a wide range of civil applications in the
last two decades. However, existing approaches, which are mainly based on
statistical properties of images, fail to detect smaller ships and boats.
Specifically, known techniques are not robust enough in view of inevitable
small geometric and photometric changes in images consisting of ships. In this
paper a novel approach for ship detection is proposed based on correlation of
maritime images. The idea comes from the observation that a fine pattern of the
sea surface changes considerably from time to time whereas the ship appearance
basically keeps unchanged. We want to examine whether the images have a common
unaltered part, a ship in this case. To this end, we developed a method -
Focused Correlation (FC) to achieve robustness to geometric distortions of the
image content. Various experiments have been conducted to evaluate the
effectiveness of the proposed approach.Comment: 8 pages, to be published in proc. of conference IEEE SMC 201
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