Related papers: Arnold diffusion in the planar elliptic restricted…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
The body of work presented here revolves around the investigation of the existence and nature of extra-solar planetary systems. The fitting of stellar radial velocity time series data is attempted by constructing a model to quantify the…
The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion…
The very long-term evolution of the hierarchical restricted three-body problem with a massive perturber is analyzed analytically in the high eccentricity regime. Perturbations on the time scale of the outer orbit can accumulate over long…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
The problem of nonintegrability of the circular restricted three-body problem is very classical and important in dynamical systems. In the first volume of his masterpieces, Henri Poincar\'e showed the nonexistence of a real-analytic first…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most…
A variety of observational evidence demonstrates that brown dwarfs exhibit active atmospheric circulations. In this study we use a shallow-water model to investigate the global atmospheric dynamics in the stratified layer overlying the…
We analyze the perturbative series of the Keldysh-type sigma-model proposed recently for describing the quantum mechanics with time-dependent Hamiltonians from the unitary Wigner-Dyson random-matrix ensemble. We observe that vertices of…
We study a stiff quasi-periodic orbit of the electromagnetic two-body problem of Dirac's electrodynamics of point charges. We expand the delay equations of motion about circular orbits to obtain the variational equations up to nonlinear…
We study the inverse problem in Optical Tomography of determining the optical properties of a medium $\Omega\subset\mathbb{R}^n$, with $n\geq 3$, under the so-called diffusion approximation. We consider the time-harmonic case where $\Omega$…
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…
Diffusion of self-propelled particles in the presence of randomly distributed obstacles in three dimensions is studied using molecular dynamics simulations. It is found that depending on the magnitude of the propelling force and the…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
Normal forms of Hamiltonian are very important to analyze the nonlinear stability of a dynamical system in the vicinity of invariant objects. This paper presents the normalization of Hamiltonian and the analysis of nonlinear stability of…
We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…
A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary…