2,674 research outputs found

### Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely
many sinksnear the generic unfolding of a quadratic homoclinic tangency of a
dissipative saddle, can be perturbed along an infinite dimensional manifold of
$C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously.
On the other hand, if they are perturbed along one-parameter families that
unfold generically the quadratic tangencies, then at most a finite number of
those sinks have continuation

### Randomised feasibility study of a novel experience-based internet intervention to support self-management in chronic asthma.

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### Infinitely Many Stochastically Stable Attractors

Let f be a diffeomorphism of a compact finite dimensional boundaryless
manifold M exhibiting infinitely many coexisting attractors. Assume that each
attractor supports a stochastically stable probability measure and that the
union of the basins of attraction of each attractor covers Lebesgue almost all
points of M. We prove that the time averages of almost all orbits under random
perturbations are given by a finite number of probability measures. Moreover
these probability measures are close to the probability measures supported by
the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure

### Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A->0 and A+B->0
when performed on scale-free networks exhibit drastically different behavior as
compared to the same reactions in normal spaces. The exponents characterizing
the density evolution as a function of time are considerably higher than 1,
implying that both reactions occur at a much faster rate. This is due to the
fact that the discerning effects of the generation of a depletion zone (A+A)
and the segregation of the reactants (A+B) do not occur at all as in normal
spaces. Instead we observe the formation of clusters of A (A+A reaction) and of
mixed A and B (A+B reaction) around the hubs of the network. Only at the limit
of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter

### Generic dynamics of 4-dimensional C2 Hamiltonian systems

We study the dynamical behaviour of Hamiltonian flows defined on
4-dimensional compact symplectic manifolds. We find the existence of a
C2-residual set of Hamiltonians for which every regular energy surface is
either Anosov or it is in the closure of energy surfaces with zero Lyapunov
exponents a.e. This is in the spirit of the Bochi-Mane dichotomy for
area-preserving diffeomorphisms on compact surfaces and its continuous-time
version for 3-dimensional volume-preserving flows

### The Economic Impacts of the Tobacco Settlement

Recent litigation against major tobacco companies culminated in a Master Settlement Agreement' (MSA) under which the participating companies agreed to compensate most states for Medicaid expenses. We outline the terms of the settlement and analyze whether it was a move toward economic efficiency using data from Massachusetts. Medicaid spending will fall, but only a modest amount ($0.1 billion). The efficiency issue turns mainly on the treatment of health benefits from reduced smoking induced by the settlement. We conclude that the settlement was a move towards economic efficiency.

### On stochastic sea of the standard map

Consider a generic one-parameter unfolding of a homoclinic tangency of an
area preserving surface diffeomorphism. We show that for many parameters
(residual subset in an open set approaching the critical value) the
corresponding diffeomorphism has a transitive invariant set $\Omega$ of full
Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets
and is accumulated by elliptic islands.
As an application we prove that stochastic sea of the standard map has full
Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure

### On the arithmetic sums of Cantor sets

Let C_\la and C_\ga be two affine Cantor sets in $\mathbb{R}$ with
similarity dimensions d_\la and d_\ga, respectively. We define an analog of
the Bandt-Graf condition for self-similar systems and use it to give necessary
and sufficient conditions for having \Ha^{d_\la+d_\ga}(C_\la + C_\ga)>0 where
C_\la + C_\ga denotes the arithmetic sum of the sets. We use this result to
analyze the orthogonal projection properties of sets of the form C_\la \times
C_\ga. We prove that for Lebesgue almost all directions $\theta$ for which the
projection is not one-to-one, the projection has zero (d_\la +
d_\ga)-dimensional Hausdorff measure. We demonstrate the results on the case
when C_\la and C_\ga are the middle-(1-2\la) and middle-(1-2\ga) sets

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