In the coming years, high-contrast imaging surveys are expected to reveal the characteristics of the population of wide-orbit, massive, exoplanets. To date, a handful of wide planetary mass companions are known, but only one such multi-planet system has been discovered: HR 8799. For low mass planetary systems, multi-planet interactions play an important role in setting system architecture. In this paper, we explore the stability of these high mass, multi-planet systems. While empirical relationships exist that predict how system stability scales with planet spacing at low masses, we show that extrapolating to super-Jupiter masses can lead to up to an order of magnitude overestimate of stability for massive, tightly packed systems. We show that at both low and high planet masses, overlapping mean-motion resonances trigger chaotic orbital evolution, which leads to system instability. We attribute some of the difference in behavior as a function of mass to the increasing importance of second order resonances at high planet-star mass ratios. We use our tailored high mass planet results to estimate the maximum number of planets that might reside in double component debris disk systems, whose gaps may indicate the presence of massive bodies.

High levels of dust have been detected in the immediate vicinity of many stars, both young and old. A promising scenario to explain the presence of this short-lived dust is that these analogues to the zodiacal cloud (or exozodis) are refilled in situ through cometary activity and sublimation. As the reservoir of comets is not expected to be replenished, the presence of these exozodis in old systems has yet to be adequately explained. It was recently suggested that mean-motion resonances with exterior planets on moderately eccentric (e(p) greater than or similar to 0.1) orbits could scatter planetesimals on to cometary orbits with delays of the order of several 100 Myr. Theoretically, this mechanism is also expected to sustain continuous production of active comets once it has started, potentially over Gyr time-scales. We aim here to investigate the ability of this mechanism to generate scattering on to cometary orbits compatible with the production of an exozodi on long time-scales. We combine analytical predictions and complementary numerical N-body simulations to study its characteristics. We show, using order of magnitude estimates, that via this mechanism, low-mass discs comparable to the Kuiper belt could sustain comet scattering at rates compatible with the presence of the exozodis which are detected around Solar-type stars, and on Gyr time-scales. We also find that the levels of dust detected around Vega could be sustained via our proposed mechanism if an eccentric Jupiter-like planet were present exterior to the system's cold debris disc.

The knowledge of the dynamics and characteristics of space plasma during solar-terrestrial coupling has been greatly enriched by process that aids the determination of the instantaneous frequencies which support the non-stationary and non-linear nature of signals. Such plasmas are observed in the magnetosheath in the downstream of bow shock. In this thesis a technique was applied which extracts the various contributing oscillatory modes reflecting the waveforms observed in the space by Cluster spacecraft instruments such as FGM, CIS and EFW, and decompose the frequency of each extracted mode using Instantaneous Frequency method that is based on Simple Hilbert Transform (SHT). This is achieved through the use of Empirical Mode Decomposition (EMD). To eliminate the negative frequency of the various extracted modes referred to as intrinsic mode function which appears with Fourier transform, we apply Hilbert transform leading to analytic representation of the signals. This process aids the determination of the instantaneous frequencies of the extracted modes. The combined process of EMD and Hilbert transform is called the Hilbert-Huang transform. The results in this thesis have been based on the improved EMD. To contribute to the understanding of plasma dynamics, the computed instantaneous frequencies are compared with the results obtained from the application of Simple Hilbert Transform. Instantaneous frequencies of overriding waves are easily separated as opposed to the application of just SHT. They offer the advantage of 3-dimensional study of the spatial characteristics of waves. The understanding of the instantaneous wave number has been achieved through the EMD and SHT combination. This provides the results which give the wave vector for a known frequency at a given instant of time. The instantaneous dispersion relation is determined using the knowledge of the instantaneous frequency and wave vector in the satellite frame, the plasma bulk velocity and the spacecraft velocity (found to be negligible compared with the plasma bulk velocity). This is accomplished using a Doppler shift relation. Wave modes identifications have been carried out by considering the proton temperature anisotropies, plasma beta and plasma bulk velocity and instantaneous phase velocity in the satellite frame. We report Alfvén mode close to the bow shock, spreading out to mirror mode which dominates the middle of magnetosheath. The mirror mode then diminishes towards the magnetopause.

In this dissertation, we demonstrate the importance of invariant objects in many areas of applied research. The areas of application we consider are chemistry, celestial mechanics and aerospace engineering, plasma physics, and coupled map lattices. In the context of chemical reactions, stable and unstable manifolds of fixed points separate regions of phase space that lead to a certain outcome of the reaction. We study how these regions change under the influence of exposing the molecules to a laser. In celestial mechanics and aerospace engineering, we compute periodic orbits and their stable and unstable manifolds for a object of negligible mass (e.g. a satellite or spacecraft) under the presence of Jupiter and two of its moons, Europa and Ganymede. The periodic orbits serve as convenient spot to place a satellite for observation purposes, and computing their stable and unstable manifolds have been used in constructing low-energy transfers between the two moons. In plasma physics, an important and practical problem is to study barriers for heat transport in magnetically confined plasma undergoing fusion. We compute barriers for which heat cannot pass through. However, such barriers break down and lead to robust partial barriers. In this latter case, heat can flow across the barrier, but at a very slow rate. Finally, infinite dimensional coupled map lattice systems are considered in a wide variety of areas, most notably in statistical mechanics, neuroscience, and in the discretization of PDEs. We assume that the interaction amont the lattice sites decays with the distance of the sites, and assume the existence of an invariant whiskered torus that is localized near a collection of lattice sites. We prove that the torus has invariant stable and unstable manifolds that are also localized near the torus. This is an important step in understanding the global dynamics of such systems and opens the door to new possible results, most notably studying the problem of energy transfer between the sites. / text

La mayor parte de los problemas de la Mecánica Celeste pueden reducirse a un problema perturbado de dos cuerpos. Esta memoria es una contribución a la comprensión y resolución de dichos problemas. En primer lugar se aborda la estructura del conjunto de órbitas del problema de dos cuerpos sin perturbar. Una adecuada definición de distancia entre órbitas permite, entre otros resultados, explicar las dificultades y singularidades que aparecen en los problemas perturbados en cuanto a las variables escogidas. Se demuestra a continuación la equivalencia formal de los métodos empleados en la teoría general de perturbaciones de la Mecánica Celeste (válidos en realidad para ecuaciones diferenciales ordinarias). Se explicitan los algoritmos que permiten el cálculo efectivo (mediante recurrencia) para todos los órdenes. En el caso del método clásico de Lagrange, Laplace y Poisson se obtienen las perturbaciones de orden cualquiera en forma explícita de manera directa. Se generaliza el teorema de Lagrange para la inversión de funciones. Su utilización es la base de diversas transformaciones. Otros conceptos introducidos en el último capítulo parecen tener interés en el estudio de la optimización y en el problema de los denominadores pequeños debidos a la dependencia de las frecuencias sobre el cuerpo racional. El detalle del contenido de los diversos capítulos se halla en la introducción que precede a cada uno de ellos. Como norma general se indica cuándo un resultado es conocido, omitiendo la demostración. Los conceptos de distancia entre órbitas, variedad de Kepler, elementos topológicos, operador de iteración, derivada contractiva, conjunto localmente accesible, desbloqueo de orden “k” y condición geométrica de desbloqueo, entre otros, se introducen en esta memoria. Si de un mismo concepto se citan varias referencias se debe a que en ellas se abordan distintos aspectos del mismo.