Shilnikov problem in Filippov dynamical systems

In this paper we introduce the concept of sliding Shilnikov orbits for $3$D Filippov systems. In short, such an orbit is a piecewise smooth closed curve, composed by Filippov trajectories, which slides on the switching surface and connects a Filippov equilibrium to itself, namely a pseudo saddle-focus. A version of the Shilnikov's Theorem is provided for such systems. Particularly, we show that sliding Shilnikov orbits occur in generic one-parameter families of Filippov systems, and that arbitrarily close to a sliding Shilnikov orbit there exist countably infinitely many sliding periodic orbits. Here, no additional Shilnikov-like assumption is needed in order to get this last result. In addition, we show the existence of sliding Shilnikov orbits in discontinuous piecewise linear differential systems. As far as we know, the examples of Fillippov systems provided in this paper are the first exhibiting such a sliding phenomenon

Some results on the use of the LANDSAT-1 multispectral images

There are no author-identified significant results in this report

Fermion Helicity Flip in Weak Gravitational Fields

The helicity flip of a spin-${\textstyle \frac{1}{2}}$ Dirac particle interacting gravitationally with a scalar field is analyzed in the context of linearized quantum gravity. It is shown that massive fermions may have their helicity flipped by gravity, in opposition to massless fermions which preserve their helicity.Comment: RevTeX 3.0, 8 pages, 3 figures (available upon request), Preprint IFT-P.013/9

Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function

Bifurcations from families of periodic solutions in piecewise differential systems

Consider a differential system of the form $$x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon),$$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times (-\varepsilon_0,\varepsilon_0) \to \mathbb{R}^m$ are piecewise $C^{k+1}$ functions and $T$-periodic in the variable $t$. Assuming that the unperturbed system $x'=F_0(t,x)$ has a $d$-dimensional submanifold of periodic solutions with $d<m$, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated $T$-periodic solutions of the above differential system

Angular Baryon Acoustic Oscillation measure at z=2.225 from the SDSS quasar survey

Following a quasi model-independent approach we measure the transversal BAO mode at high redshift using the two-point angular correlation function (2PACF). The analyses done here are only possible now with the quasar catalogue from the twelfth data release (DR12Q) from the Sloan Digital Sky Survey, because it is spatially dense enough to allow the measurement of the angular BAO signature with moderate statistical significance and acceptable precision. Our analyses with quasars in the redshift interval z = [2.20,2.25] produce the angular BAO scale theta_BAO = 1.77 +- 0.31 deg with a statistical significance of 2.12 sigma (i.e., 97% confidence level), calculated through a likelihood analysis performed using the theoretical covariance matrix sourced by the analytical power spectra expected in the LCDM concordance model. Additionally, we show that the BAO signal is robust -although with less statistical significance- under diverse bin-size choices and under small displacements of the quasars' angular coordinates. Finally, we also performed cosmological parameter analyses comparing the theta_BAO predictions for wCDM and w(a)CDM models with angular BAO data available in the literature, including the measurement obtained here, jointly with CMB data. The constraints on the parameters Omega_M, w_0 and w_a are in excellent agreement with the LCDM concordance model.Comment: 16 pages, 11 figures. To appear in JCA

The dipole anisotropy of WISE x SuperCOSMOS number counts

We probe the isotropy of the Universe with the largest all-sky photometric redshift dataset currently available, namely WISE~$\times$~SuperCOSMOS. We search for dipole anisotropy of galaxy number counts in multiple redshift shells within the $0.10 < z < 0.35$ range, for two subsamples drawn from the same parent catalogue. Our results show that the dipole directions are in good agreement with most of the previous analyses in the literature, and in most redshift bins the dipole amplitudes are well consistent with $\Lambda$CDM-based mocks in the cleanest sample of this catalogue. In the $z<0.15$ range, however, we obtain a persistently large anisotropy in both subsamples of our dataset. Overall, we report no significant evidence against the isotropy assumption in this catalogue except for the lowest redshift ranges. The origin of the latter discrepancy is unclear, and improved data may be needed to explain it.Comment: 5 pages, 4 figures, 2 tables. Published in MNRA