1,590 research outputs found
Iterated function systems with a given continuous stationary distribution
For any continuous probability measure on we construct an
IFS with probabilities having as its unique measure-attractor.Comment: 7 pages, 3 figure
Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure
For directed graph iterated function systems (IFSs) defined on R, we prove
that a class of 2-vertex directed graph IFSs have attractors that cannot be the
attractors of standard (1-vertex directed graph) IFSs, with or without
separation conditions. We also calculate their exact Hausdorff measure. Thus we
are able to identify a new class of attractors for which the exact Hausdorff
measure is known
Differentiability of fractal curves
While self-similar sets have no tangents at any single point, self-affine
curves can be smooth. We consider plane self-affine curves without double
points and with two pieces. There is an open subset of parameter space for
which the curve is differentiable at all points except for a countable set. For
a parameter set of codimension one, the curve is continuously differentiable.
However, there are no twice differentiable self-affine curves in the plane,
except for parabolic arcs
Hurst Coefficient in long time series of population size: Model for two plant populations with different reproductive strategies
Can the fractal dimension of fluctuations in population size be used to estimate extinction risk? The problem with estimating this fractal dimension is that the lengths of the time series are usually too short for conclusive results. This study answered this question with long time series data obtained from an iterative competition model. This model produces competitive extinction at different perturbation intensities for two different germination strategies: germination of all seeds vs. dormancy in half the seeds. This provided long time series of 900 years and different extinction risks. The results support the hypothesis for the effectiveness of the Hurst coefficient for estimating extinction risk
Understanding the full burden of drowning: a retrospective, cross-sectional analysis of fatal and non-fatal drowning in Australia
Objectives: The epidemiology of fatal drowning is increasingly understood. By contrast, there is relatively little population-level research on non-fatal drowning. This study compares data on fatal and non-fatal drowning in Australia, identifying differences in outcomes to guide identification of the best practice in minimising the lethality of exposure to drowning.
Design: A subset of data on fatal unintentional drowning from the Royal Life Saving National Fatal Drowning Database was compared on a like-for-like basis to data on hospital separations sourced from the Australian Institute of Health and Welfare's National Hospital Morbidity Database for the 13-year period 1 July 2002 to 30 June 2015. A restrictive definition was applied to the fatal drowning data to estimate the effect of the more narrow inclusion criteria for the non-fatal data (International Classification of Diseases (ICD) codes W65-74 and first reported cause only). Incidence and ratios of fatal to non-fatal drowning with univariate and X 2 analysis are reported and used to calculate case-fatality rates. '
Setting: Australia, 1 July 2002 to 30 June 2015.
Participants: Unintentional fatal drowning cases and cases of non-fatal drowning resulting in hospital separation.
Results: 2272 fatalities and 6158 hospital separations occurred during the study period, a ratio of 1:2.71. Children 0-4 years (1:7.63) and swimming pools (1:4.35) recorded high fatal to non-fatal ratios, whereas drownings among people aged 65-74 years (1:0.92), 75+ years (1:0.87) and incidents in natural waterways (1:0.94) were more likely to be fatal.
Conclusions: This study highlights the extent of the drowning burden when non-fatal incidents are considered, although coding limitations remain. Documenting the full burden of drowning is vital to ensuring that the issue is fully understood and its prevention adequately resourced. Further research examining the severity of non-fatal drowning cases requiring hospitalisation and tracking outcomes of those discharged will provide a more complete picture
On the "Mandelbrot set" for a pair of linear maps and complex Bernoulli convolutions
We consider the "Mandelbrot set" for pairs of complex linear maps,
introduced by Barnsley and Harrington in 1985 and studied by Bousch, Bandt and
others. It is defined as the set of parameters in the unit disk such
that the attractor of the IFS is
connected. We show that a non-trivial portion of near the imaginary axis is
contained in the closure of its interior (it is conjectured that all non-real
points of are in the closure of the set of interior points of ). Next we
turn to the attractors themselves and to natural measures
supported on them. These measures are the complex analogs of
much-studied infinite Bernoulli convolutions. Extending the results of Erd\"os
and Garsia, we demonstrate how certain classes of complex algebraic integers
give rise to singular and absolutely continuous measures . Next we
investigate the Hausdorff dimension and measure of , for
in the set , for Lebesgue-a.e. . We also obtain partial results on
the absolute continuity of for a.e. of modulus greater
than .Comment: 22 pages, 5 figure
Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals
We show that the nearest-neighbor spacing distribution for a model that
consists of random points uniformly distributed on a self-similar fractal is
the Brody distribution of random matrix theory. In the usual context of
Hamiltonian systems, the Brody parameter does not have a definite physical
meaning, but in the model considered here, the Brody parameter is actually the
fractal dimension. Exploiting this result, we introduce a new model for a
crossover transition between Poisson and Wigner statistics: random points on a
continuous family of self-similar curves with fractal dimension between 1 and
2. The implications to quantum chaos are discussed, and a connection to
conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image
available (upon request) from the author
Irreversibility in a simple reversible model
This paper studies a parametrized family of familiar generalized baker maps,
viewed as simple models of time-reversible evolution. Mapping the unit square
onto itself, the maps are partly contracting and partly expanding, but they
preserve the global measure of the definition domain. They possess periodic
orbits of any period, and all maps of the set have attractors with well defined
structure. The explicit construction of the attractors is described and their
structure is studied in detail. There is a precise sense in which one can speak
about absolute age of a state, regardless of whether the latter is applied to a
single point, a set of points, or a distribution function. One can then view
the whole trajectory as a set of past, present and future states. This
viewpoint is then applied to show that it is impossible to define a priori
states with very large "negative age". Such states can be defined only a
posteriori. This gives precise sense to irreversibility -- or the "arrow of
time" -- in these time-reversible maps, and is suggested as an explanation of
the second law of thermodynamics also for some realistic physical systems.Comment: 15 pages, 12 Postscript figure
Chaotic Scattering and Capture of Strings by Black Hole
We consider scattering and capture of circular cosmic strings by a
Schwarzschild black hole. Although being a priori a very simple axially
symmetric two-body problem, it shows all the features of chaotic scattering. In
particular, it contains a fractal set of unstable periodic solutions; a
so-called strange repellor. We study the different types of trajectories and
obtain the fractal dimension of the basin-boundary separating the space of
initial conditions according to the different asymptotic outcomes. We also
consider the fractal dimension as a function of energy, and discuss the
transition from order to chaos.Comment: RevTeX 3.1, 9 pages, 5 figure
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