Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

The First Ground Level Enhancement Event of Solar Cycle 24: Direct Observation of Shock Formation and Particle Release Heights

We report on the 2012 May 17 Ground Level Enhancement (GLE) event, which is the first of its kind in Solar Cycle 24. This is the first GLE event to be fully observed close to the surface by the Solar Terrestrial Relations Observatory (STEREO) mission. We determine the coronal mass ejection (CME) height at the start of the associated metric type II radio burst (i.e., shock formation height) as 1.38 Rs (from the Sun center). The CME height at the time of GLE particle release was directly measured from a STEREO image as 2.32 Rs, which agrees well with the estimation from CME kinematics. These heights are consistent with those obtained for cycle-23 GLEs using back-extrapolation. By contrasting the 2012 May 17 GLE with six other non-GLE eruptions from well-connected regions with similar or larger flare size and CME speed, we find that the latitudinal distance from the ecliptic is rather large for the non-GLE events due to a combination of non-radial CME motion and unfavorable solar B0 angle, making the connectivity to Earth poorer. We also find that the coronal environment may play a role in deciding the shock strength.Comment: 16 pages, 4 figures, 1 tabl

Lyman Break Galaxies at z∼5z\sim5: Rest-Frame UV Spectra

We report initial results for spectroscopic observations of candidates of Lyman Break Galaxies (LBGs) at $z\sim5$ in a region centered on the Hubble Deep Field-North by using the Faint Object Camera and Spectrograph attached to the Subaru Telescope. Eight objects with $I_C\leq25.0$ mag, including one AGN, are confirmed to be at $4.5<z<5.2$. The rest-frame UV spectra of seven LBGs commonly show no or weak Lyalpha emission line (rest-frame equivalent width of 0-10\AA) and relatively strong low-ionization interstellar metal absorption lines of SiII $\lambda$1260, OI+SiII $\lambda$1303, and CII $\lambda$1334 (mean rest-frame equivalent widths of them are $-1.2 \sim -5.1$\AA). These properties are significantly different from those of the mean rest-frame UV spectrum of LBGs at $z\sim3$, but are quite similar to those of subgroups of LBGs at $z\sim3$ with no or weak Lyalpha emission. The weakness of Lyalpha emission and strong low-ionization interstellar metal absorption lines may indicate that these LBGs at $z\sim5$ are chemically evolved to some degree and have a dusty environment. Since the fraction of such LBGs at $z\sim5$ in our sample is larger than that at $z\sim3$, we may witness some sign of evolution of LBGs from $z\sim5$ to $z\sim3$, though the present sample size is very small. It is also possible, however, that the brighter LBGs tend to show no or weak Lyalpha emission, because our spectroscopic sample is bright (brighter than $L^{\ast}$) among LBGs at $z\sim5$. More observations are required to establish spectroscopic nature of LBGs at $z\sim5$.Comment: 16 pages, 3 figures, accepted by Ap

Boundaries of Disk-like Self-affine Tiles

Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the paper, we identify the boundary $\partial T$ with a sofic system by constructing a neighbor graph and derive equivalent conditions for the pair $(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed construction and a device of pseudo-norm $\omega$, we find the generalized Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where $\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially, when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H (\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than the known result.Comment: 26 pages, 11 figure

Controlling chaotic transients: Yorke's game of survival

5 pages, 4 figures.-- PACS nr.: 05.45.Gg, 05.45.Pq.-- PMID: 14995689 [PubMed].We consider the tent map as the prototype of a chaotic system with escapes. We show analytically that a small, bounded, but carefully chosen perturbation added to the system can trap forever an orbit close to the chaotic saddle, even in presence of noise of larger, although bounded, amplitude. This problem is focused as a two-person, mathematical game between two players called "the protagonist" and "the adversary." The protagonist's goal is to survive. He can lose but cannot win; the best he can do is survive to play another round, struggling ad infinitum. In the absence of actions by either player, the dynamics diverge, leaving a relatively safe region, and we say the protagonist loses. What makes survival difficult is that the adversary is allowed stronger "actions" than the protagonist. What makes survival possible is (i) the background dynamics (the tent map here) are chaotic and (ii) the protagonist knows the action of the adversary in choosing his response and is permitted to choose the initial point x(0) of the game. We use the "slope 3" tent map in an example of this problem. We show that it is possible for the protagonist to survive.J.A. and M.S.J. acknowledge financial support from the Spanish Ministry of Science and Technology under project BFM2000-0967, and from the Universidad Rey Juan Carlos under projects URJC-PGRAL-2001/02 and URJC-PIGE-02-04. F.d'O. acknowledges financial support from MCyT (Spain) and FEDER, project REN2001-0802-C02-01/MAR (IMAGEN).Peer reviewe

The Magnetorotational Instability in Core Collapse Supernova Explosions

We investigate the action of the magnetorotational instability (MRI) in the context of iron-core collapse. Exponential growth of the field on the rotation time scale by the MRI will dominate the linear growth process of field line "wrapping" with the same characteristic time. We examine a variety of initial rotation states, with solid body rotation or a gradient in rotational velocity, that correspond to models in the literature. A relatively modest value of the initial rotation, a period of ~ 10 s, will give a very rapidly rotating PNS and hence strong differential rotation with respect to the infalling matter. We assume conservation of angular momentum on spherical shells. Results are discussed for two examples of saturation fields, a fiducial field that corresponds to Alfven velocity = rotational velocity and a field that corresponds to the maximum growing mode of the MRI. Modest initial rotation velocities of the iron core result in sub-Keplerian rotation and a sub-equipartition magnetic field that nevertheless produce substantial MHD luminosity and hoop stresses: saturation fields of order 10^{15} - 10^{16} G develop within 300 msec after bounce with an associated MHD luminosity of about 10^{52} erg/s. Bi-polar flows driven by this MHD power can affect or even cause the explosions associated with core-collapse supernovae.Comment: 42 pages, including 15 figures. Accepted for publication in ApJ. We have revised to include an improved treatment of the convection, and some figures have been update