Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

A method to find unstable periodic orbits for the diamagnetic Kepler problem

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable manifolds. By investigating the unstable periodic orbits up to length 6, a one to one correspondence between the unstable periodic orbits and their corresponding symbolic sequences is shown under the system symmetry decomposition.

The dynamic evolution of the kepler supernova remnant

been analyzed in detail. The effects ofm icroscopic energy transfer from

Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with an appropriate momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The trajectories lie on ellipses. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and extends to o(4,2). (c) 2010 Elsevier B.V. All rights reserved.

Estimating Stellar Radial Velocity Variability from Kepler and GALEX: Implications for the radial velocity confirmation of exoplanets.

We cross match the GALEX and Kepler surveys to create a unique dataset with both ultraviolet (UV) measurements and highly precise photometric variability measurements in the visible light spectrum. As stellar activity is driven by magnetic field modulations, we have used UV emission from the magnetically heated gas in the stellar atmosphere to serve as our proxy for the more well-known stellar activity indicator, R' HK . The R' HK approximations were in turn used to estimate the level of astrophysical noise expected in radial velocity (RV) measurements and these were then searched for correlations with photometric variability. We find significant scatter in our attempts to estimate RV noise for magnetically active stars, which we attribute to variations in the phase and strength of the stellar magnetic cycle that drives the activity of these targets. However, for stars we deem to be magnetically quiet, we do find a clear correlation between photometric variability and estimated levels of RV noise (with variability up to ~10 m s–1). We conclude that for these quiet stars, we can use photometric measurements as a proxy to estimate the RV noise expected. As a result, the procedure outlined in this paper may help select targets best-suited for RV follow-up necessary for planet confirmation.

The Kepler-10 Planetary System Revisited by HARPS-N: A Hot Rocky World and a Solid Neptune-Mass Planet

Kepler-10b was the first rocky planet detected by the Kepler satellite and confirmed with radial velocity follow-up observations from Keck-HIRES. The mass of the planet was measured with a precision of around 30%, which was
insufficient to constrain models of its internal structure and composition in detail. In addition to Kepler-10b, a second planet transiting the same star with a period of 45 days was statistically validated, but the radial velocities were only
good enough to set an upper limit of 20 M⊕ for the mass of Kepler-10c. To improve the precision on the mass for planet b, the HARPS-N Collaboration decided to observe Kepler-10 intensively with the HARPS-N spectrograph
on the Telescopio Nazionale Galileo on La Palma. In total, 148 high-quality radial-velocity measurements were obtained over two observing seasons. These new data allow us to improve the precision of the mass determination for Kepler-10b to 15%. With a mass of 3.33 ± 0.49 M⊕ and an updated radius of 1.47+0.03 −0.02 R⊕, Kepler-10b has a density of 5.8 ± 0.8 g cm−3, very close to the value predicted by models with the same internal structure and composition as the Earth. We were also able to determine a mass for the 45-day period planet Kepler-10c, with an even better precision of 11%. With a mass of 17.2 ± 1.9 M⊕ and radius of 2.35+0.09 −0.04 R⊕, Kepler-10c has a density of 7.1 ± 1.0 g cm−3. Kepler-10c appears to be the first strong evidence of a class of more massive solid planets with longer orbital periods

Characterization of the Kepler-101 planetary system with HARPS-N. A hot super-Neptune with an Earth-sized low-mass companion

We characterize the planetary system Kepler-101 by performing a combined differential evolution Markov chain Monte Carlo analysisof Kepler data and forty radial velocities obtained with the HARPS-N spectrograph. This system was previously validated and iscomposed of a hot super-Neptune, Kepler-101b, and an Earth-sized planet, Kepler-101c. These two planets orbit the slightly evolvedand metal-rich G-type star in 3.49 and 6.03 days, respectively. With mass Mp = 51.1+5.1−4.7 M⊕, radius Rp = 5.77+0.85−0.79 R⊕, and density ρp = 1.45+0.83 −0.48 g cm−3, Kepler-101b is the first fully characterized super-Neptune, and its density suggests that heavy elements makeup a significant fraction of its interior; more than 60% of its total mass. Kepler-101c has a radius of 1.25+0.19−0.17 R⊕, which implies theabsence of any H/He envelope, but its mass could not be determined because of the relative faintness of the parent star for highly precise radial-velocity measurements (Kp = 13.8) and the limited number of radial velocities. The 1σ upper limit, Mp < 3.8 M⊕, excludes a pure iron composition with a probability of 68.3%. The architecture of the planetary system Kepler-101 − containing aclose-in giant planet and an outer Earth-sized planet with a period ratio slightly larger than the 3:2 resonance − is certainly of interest for scenarios of planet formation and evolution. This system does not follow the previously reported trend that the larger planet has the longer period in the majority of Kepler systems of planet pairs with at least one Neptune-sized or larger planet.

Épistémologie du concept d'harmonie dans les recherches scientifiques de Kepler

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

L'astronomie nouvelle de Kepler et la logique de la découverte

Cette thèse propose une étude des raisons théoriques et empiriques impliquées dans l’élaboration d’une nouvelle astronomie par Johannes Kepler (1571-1630) tel qu’exposé dans son ouvrage Astronomia nova (1619). Cette thèse se déroule en deux temps : la première partie touche de près aux textes mêmes de Kepler, tandis que la seconde partie utilise la notion d’abduction pour interpréter logiquement ce processus de découverte et de justification. La première partie débute avec une analyse du projet de Kepler et de ses fondements philosophiques, métaphysiques et théologiques tels qu’exposés dans son premier ouvrage, le Mysterium cosmographicum. Ensuite, une étude des propos explicites de Kepler quant à la nature et au statut des hypothèses astronomiques est proposée via une étude de son traité intitulé Apologia pro Tychone contra Ursum. Une étude attentive des sources philosophiques, mathématiques et scientifiques ayant influencé Kepler pour sa nouvelle astronomie est ensuite proposée avant l’analyse détaillée des arguments scientifiques et des différentes étapes démonstratives qui sont présentés dans l’Astronomia nova. La deuxième partie vise à éclairer le débat sur l’abduction en se penchant d’abord sur trois approches traditionnelles (Platon, Aristote et Épicure) quant à la connaissance scientifique des phénomènes célestes permettant d’obtenir un discours vraisemblable ou une multiplicité d’explications concordantes avec les phénomènes. Enfin, quatre interprétations contemporaines et abductives du processus de découverte suivi par Kepler dans l’Astronomia nova sont présentées, reformulées et critiquées afin de proposer une nouvelle interprétation abductive laissant une plus grande place au projet même de construire une astronomie nouvelle fondée sur les causes. Cela nous donne des outils pour mieux saisir le sens et la portée de ce qui peut être désigné comme étant la « révolution képlérienne », soit le passage d’un système géocentrique à un système non pas simplement héliocentrique mais héliodynamique, ayant permis aux astronomes de s’affranchir du paradigme des orbites circulaires.

Kepler.

Programa sobre MS-DOS para Física de COU. Simula las tres leyes de Kepler sobre un satélite alrededor de la Tierra. Partiendo de unas condiciones iniciales calcula la ecuación diferencial y presenta gráficamente las nuevas posiciones. Incluye manual que incorpora el uso del programa y las utilidades pedagógicas, llegando a poder utilizarse en Filosofía para el tema de la revolución copérnica.

Innovación docente en el marco de cumplimiento de los estándares de desempeño profesional estipulados por el Ministerio de Educación, en el colegio Johannes Kepler

No es suficiente una encuesta o como en este caso tres, para adentrarse en el bosque de alternativas que el proceso educativo encierra, sin embargo pretendo con este estudio analizar el efecto de una estructura (Reforma educativa del 2010 Ecuador) que puede involucrar cambios significativos, que supone transformación y variaciones cualitativas relevantes; por lo que el objetivo que tiene esta investigación es determinar cómo el cumplimiento de estándares y la formulación de documentos por parte de los docentes del Colegio Johannes Kepler afecta a las diferentes gestiones relacionadas con el proceso educativo y cómo la puesta en marcha de un planteamiento teórico pensado y diseñado por un reducido grupo social, implica a sus participantes a concertar, planificar, determinar procesos y procedimientos que requieren ser mediados por las autoridades de cada institución, con un acompañamiento atento y persistente, que podría equilibrar la gestión integral del sistema educativo y en especial la gestión docente en el aula; sin perder la creatividad para seleccionar, implementar experiencias formativas que desafíen a los estudiantes a ser resilientes y críticos, a través de prácticas significativas que les permita integrar nuevos aprendizajes y mejorar sus relaciones interpersonales. Este trabajo tiene como intención dar luces a todos los lectores, educadores y directivos de los diferentes establecimientos educativos, para encontrar un balance en la gestión administrativa y “la razón de ser” de toda institución educativa que es formar seres humanos competentes socialmente y no solamente reformular evidencias administrativas para llegar a ser más eficientes y eficaces en un proceso que necesita sabiduría y equilibrio para dejar una huella y revolucionar un sistema. Además, pretendo dilucidar la influencia que vive el docente, en su práctica cotidiana que tiene como marco de acción estándares que miden su conocimiento y dominio de los lineamientos curriculares determinados a nivel nacional, que permiten a sus protagonistas (los maestros/as ecuatorianos/as) analizar el alcance de la gestión de aprendizaje, su capacitación y su compromiso ético profesional, y que les lleva en su gestión pedagógica a ser creativos e innovadores esencialmente en el proceso de enseñanza aprendizaje, a promover políticas y estrategias que permitan potenciar una cultura orientada hacia el cambio, aplicando un enfoque flexible, integrado, interdisciplinario y crítico en su intervención en el aula.

O enigmático problema das gigantes ricas em Lítio e as perspectivas com o satélite Kepler

Lithium (Li) is a chemical element with atomic number 3 and it is among the lightest known elements in the universe. In general, the Lithium is found in the nature under the form of two stable isotopes, the 6Li and 7Li. This last one is the most dominant and responds for about 93% of the Li found in the Universe. Due to its fragileness this element is largely used in the astrophysics, especially in what refers to the understanding of the physical process that has occurred since the Big Bang going through the evolution of the galaxies and stars. In the primordial nucleosynthesis in the Big Bang moment (BBN), the theoretical calculation forecasts a Li production along with all the light elements such as Deuterium and Beryllium. To the Li the BNB theory reviews a primordial abundance of Log log ǫ(Li) =2.72 dex in a logarithmic scale related to the H. The abundance of Li found on the poor metal stars, or pop II stars type, is called as being the abundance of Li primordial and is the measure as being log ǫ(Li) =2.27 dex. In the ISM (Interstellar medium), that reflects the current value, the abundance of Lithium is log ǫ(Li) = 3.2 dex. This value has great importance for our comprehension on the chemical evolution of the galaxy. The process responsible for the increasing of the primordial value present in the Li is not clearly understood until nowadays. In fact there is a real contribution of Li from the giant stars of little mass and this contribution needs to be well streamed if we want to understand our galaxy. The main objection in this logical sequence is the appearing of some giant stars with little mass of G and K spectral types which atmosphere is highly enriched with Li. Such elevated values are exactly the opposite of what could happen with the typical abundance of giant low mass stars, where convective envelops pass through a mass deepening in which all the Li should be diluted and present abundances around log ǫ(Li) ∼1.4 dex following the model of stellar evolution. In the Literature three suggestions are found that try to reconcile the values of the abundance of Li theoretical and observed in these rich in Li giants, but any of them bring conclusive answers. In the present work, we propose a qualitative study of the evolutionary state of the rich in Li stars in the literature along with the recent discovery of the first star rich in Li observed by the Kepler Satellite. The main objective of this work is to promote a solid discussion about the evolutionary state based on the characteristic obtained from the seismic analysis of the object observed by Kepler. We used evolutionary traces and simulation done with the population synthesis code TRILEGAL intending to evaluate as precisely as possible the evolutionary state of the internal structure of these groups of stars. The results indicate a very short characteristic time when compared to the evolutionary scale related to the enrichment of these stars

A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action

A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.