Related papers: Scattered Disk Dynamics: The Mapping Approach
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization…
Planets in extrasolar systems tend to interact such that their orbits lie near a boundary between apsidal libration and circulation, a "separatrix", with one eccentricity periodically reaching near-zero. One explanation, applied to the…
Many interesting physical systems have mathematical descriptions as finite-dimensional or infinite-dimensional Hamiltonian systems. Poincare who started the modern theory of dynamical systems and symplectic geometry developed a particular…
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
Resolved images suggest that asymmetric structures are a common feature of cold debris disks. While planets close to these disks are rarely detected, their hidden presence and gravitational perturbations provide plausible explanations for…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
Geometric mechanics provides valuable insights into how biological and robotic systems use changes in shape to move by mechanically interacting with their environment. In high-friction environments it provides that the entire interaction is…
There is an effect in the modified dynamics (MOND) that is conducive to formation of warps. Because of the nonlinearity of the theory the internal dynamics of a galaxy is affected by a perturber over and above possible tidal effects. For…
We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function $f$. We…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…
Drastic changes in protoplanets' orbits could occur in the early stages of planetary systems through interactions with other planets and their surrounding protoplanetary or debris discs. The resulting planetary system could exhibit orbits…
Numerical integrations of the Solar System have been carried out for decades. Their results have been used, for example, to determine whether the Solar System is chaotic, whether Mercury's orbit is stable, or to help discern Earth's climate…
Symplectic maps are routinely used to describe single-particle dynamics in circular accelerators. In the case of a linear accelerator map, the rotation number (the betatron frequency) can be easily calculated from the map itself. In the…
We study orbital inclination changes associated with the precession of a disc-planet system that occurs through gravitational interaction with a binary companion on an inclined orbit. We investigate whether this scenario can account for…
The gravitational influence of a planet on a nearby disk provides a powerful tool for detecting and studying extrasolar planetary systems. Here we demonstrate that gaps can be opened in dynamically cold debris disks at the mean-motion…
This paper explores the intermediate-time dynamics of newly formed solar systems with a focus on possible mechanisms for planetary migration. We consider two limiting corners of the available parameter space -- crowded systems containing…