12,337 research outputs found
Statistical stability and limit laws for Rovella maps
We consider the family of one-dimensional maps arising from the contracting
Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used
by Rovella to prove that there is a one-parameter family of maps whose
derivatives along their critical orbits increase exponentially fast and the
critical orbits have slow recurrent to the critical point. Metzger proved that
these maps have a unique absolutely continuous ergodic invariant probability
measure (SRB measure).
Here we use the technique developed by Freitas and show that the tail set
(the set of points which at a given time have not achieved either the
exponential growth of derivative or the slow recurrence) decays exponentially
fast as time passes. As a consequence, we obtain the continuous variation of
the densities of the SRB measures and associated metric entropies with the
parameter. Our main result also implies some statistical properties for these
maps.Comment: 1 figur
Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations
We consider globally invertible and piecewise contracting maps in higher
dimensions and we perturb them with a particular kind of noise introduced by
Lasota and Mackey. We got random transformations which are given by a
stationary process: in this framework we develop an extreme value theory for a
few classes of observables and we show how to get the (usual) limiting
distributions together with an extremal index depending on the strength of the
noise.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1407.041
Dynamics of a superconducting qubit coupled to the quantized cavity field: a unitary transformation approach
We present a novel approach for studying the dynamics of a superconducting
qubit in a cavity. We succeed in linearizing the Hamiltonian through the
application of an appropriate unitary transformation followed by a rotating
wave approximation (RWA). For certain values of the parameters involved, we
show that it is possible to obtain a a Jaynes-Cummings type Hamiltonian. As an
example, we show the existence of super-revivals for the qubit inversion
A Random Multifractal Tilling
We develop a multifractal random tilling that fills the square. The
multifractal is formed by an arrangement of rectangular blocks of different
sizes, areas and number of neighbors. The overall feature of the tilling is an
heterogeneous and anisotropic random self-affine object. The multifractal is
constructed by an algorithm that makes successive sections of the square. At
each -step there is a random choice of a parameter related to the
section ratio. For the case of random choice between and we
find analytically the full spectrum of fractal dimensions
Anisotropy and percolation threshold in a multifractal support
Recently a multifractal object, , was proposed to study percolation
properties in a multifractal support. The area and the number of neighbors of
the blocks of show a non-trivial behavior. The value of the
probability of occupation at the percolation threshold, , is a function
of , a parameter of which is related to its anisotropy. We
investigate the relation between and the average number of neighbors of
the blocks as well as the anisotropy of
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