1,033 research outputs found
Social Implications of Teenage Parenthood
Contrary to popular impression, the absolute level of teenage childbearing in the United States has not risen during the past decade, but has actually declined. Moreover, the newly discovered epidemic of adolescent pregnancy is not recent; elevated levels of teenage childbearing can be traced to the beginning of the baby boom after the Second World War. Nevertheless, the issue does seem more pressing now than ever before. In this chapter we shall touch on some of the reasons for this issue\u27s prominence. We shall look at the evidence in the literature on the social consequences of teenage childbearing for adolescent parents, their offspring, and members of their family of origin. After assessing this evidence, we shall briefly mention some of the policy initiatives open for us for preventing premature childbearing and for ameliorating its deleterious effects when it does occur
The triangle map: a model of quantum chaos
We study an area preserving parabolic map which emerges from the Poincar\' e
map of a billiard particle inside an elongated triangle. We provide numerical
evidence that the motion is ergodic and mixing. Moreover, when considered on
the cylinder, the motion appear to follow a gaussian diffusive process.Comment: 4 pages in RevTeX with 4 figures (in 6 eps-files
Singularity results for functional equations driven by linear fractional transformations
We consider functional equations driven by linear fractional transformations,
which are special cases of de Rham's functional equations. We consider
Hausdorff dimension of the measure whose distribution function is the solution.
We give a necessary and sufficient condition for singularity. We also show that
they have a relationship with stationary measures.Comment: 14 pages, Title changed, to appear in Journal of Theoretical
Probabilit
Ray splitting in paraxial optical cavities
We present a numerical investigation of the ray dynamics in a paraxial
optical cavity when a ray splitting mechanism is present. The cavity is a
conventional two-mirror stable resonator and the ray splitting is achieved by
inserting an optical beam splitter perpendicular to the cavity axis. We show
that depending on the position of the beam splitter the optical resonator can
become unstable and the ray dynamics displays a positive Lyapunov exponent.Comment: 13 pages, 7 figures, 1 tabl
Real extensions of distal minimal flows and continuous topological ergodic decompositions
We prove a structure theorem for topologically recurrent real skew product
extensions of distal minimal compact metric flows with a compactly generated
Abelian acting group (e.g. -flows and -flows). The main result
states that every such extension apart from a coboundary can be represented by
a perturbation of a so-called Rokhlin skew product. We obtain as a corollary
that the topological ergodic decomposition of the skew product extension into
prolongations is continuous and compact with respect to the Fell topology on
the hyperspace. The right translation acts minimally on this decomposition,
therefore providing a minimal compact metric analogue to the Mackey action.
This topological Mackey action is a distal (possibly trivial) extension of a
weakly mixing factor (possibly trivial), and it is distal if and only if
perturbation of the Rokhlin skew product is defined by a topological
coboundary.Comment: This paper is an extension and generalisation of
http://arxiv.org/abs/0909.0192. The result has been generalised from actions
of the group of integers to actions of Abelian compactly generated
transformation groups. Therefore the title had to be changed (homeomorphisms
vs. flows
Exact Lyapunov Exponent for Infinite Products of Random Matrices
In this work, we give a rigorous explicit formula for the Lyapunov exponent
for some binary infinite products of random real matrices. All
these products are constructed using only two types of matrices, and ,
which are chosen according to a stochastic process. The matrix is singular,
namely its determinant is zero. This formula is derived by using a particular
decomposition for the matrix , which allows us to write the Lyapunov
exponent as a sum of convergent series. Finally, we show with an example that
the Lyapunov exponent is a discontinuous function of the given parameter.Comment: 1 pages, CPT-93/P.2974,late
Nonconventional Large Deviations Theorems
We obtain large deviations theorems for nonconventional sums with underlying
process being a Markov process satisfying the Doeblin condition or a dynamical
system such as subshift of finite type or hyperbolic or expanding
transformation
Symbolic approach and induction in the Heisenberg group
We associate a homomorphism in the Heisenberg group to each hyperbolic
unimodular automorphism of the free group on two generators. We show that the
first return-time of some flows in "good" sections, are conjugate to
niltranslations, which have the property of being self-induced.Comment: 18 page
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