Related papers: Scattered Disk Dynamics: The Mapping Approach
Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…
We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. We use the symplectic integrator SyMBA to numerically…
We study diffusion in a one-dimensional periodic array of scatterers modeled by a simple map. The chaotic scattering process for this map can be changed by a control parameter and exhibits the dynamics of a crisis in chaotic scattering. We…
The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption of gravitational radiation is investigated. This work extends our previous results on transient chaos in the planar case to the three…
We review previous results providing sufficient conditions to determine the global dynamics for equivariant maps of the plane with a unique fixed point which is also hyperbolic.
We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in…
A 3D-dynamical model is constructed for the study of motion in the central regions of a disk galaxy with a double nucleus. Using the results of the 2D-model, we find the regions of initial conditions in the (x,px,z,py)=EJ, (y=pz=0) phase…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
Using experimental techniques, we study properties of the "circumcenter map", which, upon $n$ iterations sends an $n$-gon to a scaled and rotated copy of itself. We also explore the topology of area-expanding and area-contracting regions…
We construct a simple symplectic map to study the dynamics of eccentric orbits in non-spherical potentials. The map offers a dramatic improvement in speed over traditional integration methods, while accurately representing the qualitative…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
We present a novel approach for studying the global dynamics of a vibro-impact pair, that is, a ball moving in a harmonically forced capsule. Motivated by a specific context of vibro-impact energy harvesting, we develop the method with…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
We consider how the reduced dynamics of an open quantum system coupled to an environment admits the Poincar\'e symmetry. The reduced dynamics is described by a dynamical map, which is given by tracing out the environment from the total…
We show that interaction with a gas disk may produce young planetary systems with closely-spaced orbits, stabilized by mean-motion resonances between neighbors. On longer timescales, after the gas is gone, interaction with a remnant…
A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers…
Interaction of electromagnetic, acoustic and even gravitational waves with accelerating bodies forms a class of nonstationary time-variant processes. Scattered waves contain intrinsic signatures of motion, which manifest in a broad range of…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…
Compact multi-planet systems containing super-Earths or sub-Neptunes, commonly found around solar-type stars, may be surrounded by external giant planet or stellar companions, which can shape the architechture and observability of the inner…