Related papers: Scattered Disk Dynamics: The Mapping Approach
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, including a period doubling route to chaos. By approximating the…
A large sample of planet-planet scattering events for three planet systems with different orbital separations and masses is analyzed with a multiple regression model. The dependence of the time for the onset of instability on the masses of…
The circular restricted three body problem is investigated in the context of accretion and scattering processes. In our model a large number of identical non-interacting mass-less planetesimals are considered in planar case orbiting a…
We consider the planar circular restricted three-body problem (PCRTBP), as a model for the motion of a spacecraft relative to the Earth-Moon system. We focus on the Lagrange equilibrium points $L_1$ and $L_2$. There are families of Lyapunov…
The majority of the discovered transiting circumbinary planets are located very near the innermost stable orbits permitted, raising questions about the origins of planets in such perturbed environments. Most favored formation scenarios…
Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form…
The standard formation model of close-in low-mass planets involves efficient inward migration followed by growth through giant impacts after the protoplanetary gas disk disperses. While detailed N-body simulations have enhanced our…
Observational manifestations of disturbances in a protoplanetary disk caused by a collision with a massive planet are studied. It is assumed that the planet moves along a parabolic trajectory that intersects the disk plane near the star.…
Observations of clustering among the orbits of the most distant trans-Neptunian objects (TNOs) has inspired interest in the possibility of an undiscovered ninth planet lurking in the outskirts of the solar system. Numerical simulations by a…
Models of debris disk morphology are often focused on the effects of a planet orbiting interior to or within the disk. Nonetheless, an exterior planetary-mass perturber can also excite eccentricities in a debris disk, via Laplace-Lagrange…
We study the closed Hamiltonian dynamics of a free particle moving on a ring, over one section of which it interacts linearly with a single harmonic oscillator. On the basis of numerical and analytical evidence, we conjecture that at small…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
The aim of this talk is to present the most recent advances in establishing plausible planetary system architectures determined by the gravitational tidal interactions between the planets and the disc in which they are embedded during the…
The regular or chaotic dynamics of an analytical realistic three dimensional model composed of a spherically symmetric central nucleus, a bar and a flat disk is investigated. For describing the properties of the bar we introduce a new…
In this paper we study dynamical properties of the area preserving Henon map, as a discrete version of open Hamiltonian systems, that can exhibit chaotic scattering. Exploiting its geometric properties we locate the exit and entry sets,…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for…
The increasing threat raised by space debris led to the development of different mathematical models and approaches to investigate the dynamics of small particles orbiting around the Earth. Such models and methods strongly depend on the…