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

Strong evidences for a nonextensive behavior of the rotation period in Open Clusters

Time-dependent nonextensivity in a stellar astrophysical scenario combines nonextensive entropic indices $q_{K}$ derived from the modified Kawaler's parametrization, and $q$, obtained from rotational velocity distribution. These $q$'s are related through a heuristic single relation given by $q\approx q_{0}(1-\Delta t/q_{K})$, where $t$ is the cluster age. In a nonextensive scenario, these indices are quantities that measure the degree of nonextensivity present in the system. Recent studies reveal that the index $q$ is correlated to the formation rate of high-energy tails present in the distribution of rotation velocity. On the other hand, the index $q_{K}$ is determined by the stellar rotation-age relationship. This depends on the magnetic field configuration through the expression $q_{K}=1+4aN/3$, where $a$ and $N$ denote the saturation level of the star magnetic field and its topology, respectively. In the present study, we show that the connection $q-q_{K}$ is also consistent with 548 rotation period data for single main-sequence stars in 11 Open Clusters aged less than 1 Gyr. The value of $q_{K}\sim$ 2.5 from our unsaturated model shows that the mean magnetic field topology of these stars is slightly more complex than a purely radial field. Our results also suggest that stellar rotational braking behavior affects the degree of anti-correlation between $q$ and cluster age $t$. Finally, we suggest that stellar magnetic braking can be scaled by the entropic index $q$.Comment: 6 pages and 2 figures, accepted to EPL on October 17, 201

Imagery and long-slit spectroscopy of the Polar-Ring Galaxy AM2020-504

Interactions between galaxies are very common. There are special kinds of interactions that produce systems called Polar Ring Galaxies (PRGs), composed by a lenticular, elliptical, or spiral host galaxy, surrounded by a ring of stars and gas, orbiting in an approximately polar plane. The present work aims to study AM2020-504, a PRG with an elliptical host galaxy, and a narrow and well defined ring, probably formed by accretion of material from a donor galaxy, collected by the host galaxy. Our observational study was based on BVRI broad band imagery as well as longslit spectroscopy in the wavelenght range 4100--8600\AA, performed at the 1.6m telescope at the Observat\'orio do Pico dos Dias (OPD), Brazil. We estimated a redshift of z= 0.01683, corresponding a heliocentric radial velocity of 5045 +/-23 km/s. The (B-R) color map shows that the ring is bluer than the host galaxy, indicating that the ring is a younger structure. Standard diagnostic diagrams were used to classify the main ionizing source of selected emission-line regions (nucleus, host galaxy and ring). It turns out that the ring regions are mainly ionized by massive stars while the nucleus presents AGN characteristics. Using two empirical methods, we found oxygen abundances for the HII regions located in the ring in the range 12+log(O/H)=8.3-8.8 dex, the presence of an oxygen gradient across the ring, and that AM2020-504 follows the metallicity-luminosity relation of spiral galaxies. These results support the accretion scenario for this object and rules out cold accretion as source for the HI gas in the polar ring

Statistical stability of equilibrium states for interval maps

We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential $\phi_t:x\mapsto-t\log|Df(x)|$, for $t$ close to 1. We show that these equilibrium states vary continuously in the weak$^*$ topology within such families. Moreover, in the case $t=1$, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities vary continuously within these families.Comment: More details given and the appendices now incorporated into the rest of the pape

A nonextensive insight to the stellar initial mass function

the present paper, we propose that the stellar initial mass distributions as known as IMF are best fitted by $q$-Weibulls that emerge within nonextensive statistical mechanics. As a result, we show that the Salpeter's slope of $\sim$2.35 is replaced when a $q$-Weibull distribution is used. Our results point out that the nonextensive entropic index $q$ represents a new approach for understanding the process of the star-forming and evolution of massive stars.Comment: 5 pages, 2 figures, Accepted to EP

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Disorder effects at low temperatures in La_{0.7-x}Y_{x}Ca_{0.3}MnO_{3} manganites

With the aim of probing the effect of magnetic disorder in the low-temperature excitations of manganites, specific-heat measurements were performed in zero field, and in magnetic fields up to 9 T in polycrystalline samples of La_{0.7-x}Y_{x}Ca_{0.3}MnO_{3}, with Y concentrations x=0, 0.10, and 0.15. Yttrium doping yielded the appearance of a cluster-glass state, giving rise to unusual low-temperature behavior of the specific-heat. The main feature observed in the results is a strong enhancement of the specific-heat linear term, which is interpreted as a direct consequence of magnetic disorder. The analysis was further corroborated by resistivity measurements in the same compounds.Comment: 9 pages, 2 figure