Related papers: Properties of some dynamical systems for three col…
M. Kruskal showed that each nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of each order, near which rapid…
Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital…
We characterize a system of tilted dipoles in a quasi two-dimensional (flattened) geometry and in the thermodynamic limit. We consider a finite trapping in the z-axis achievable in current experiments. We compute the phase diagram of the…
Everything you ever wanted to know about what has come to be known as ``chaotic mixing:'' This paper describes the evolution of localised ensembles of initial conditions in 2- and 3-D time-independent potentials which admit both regular and…
The possibility of generating stable anisotropic solitons in dipolar Bose-Einstein condensates (BECs) leads to a different scenario not possible in a nondipolar BEC with contact interaction. We study the statics and dynamics of anisotropic…
We obtain an expression for the energy of the density wave propagating in a multicomponent gravitating medium in the form well known from electrodynamics. Using the above, the possibility of "triple production" of the quasi-particles, or…
A two-dimensional system of particles with tunable repulsive interactions is experimentally investigated. Soft ferromagnetic particles are placed on a vibrating rough plate and vertically confined, so that they perform a horizontal Brownian…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
A heterodimensional cycle consists of a pair of heteroclinic connections between two saddle periodic orbits with unstable manifolds of different dimensions. Recent theoretical work on chaotic dynamics beyond the uniformly hyperbolic setting…
Consider a dynamic general relativistic spacetime in which the proper infinitesimal interval along one spatial coordinate direction decreases monotonically with time, while the corresponding intervals increase along other spatial…
We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a…
The orientational dynamics of inertialess anisotropic particles transported by two-dimensional convective turbulent flows display a coexistence of regular and chaotic features. We numerically demonstrate that very elongated particles (rods)…
The superlubric-pinned transition in the depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by 2D triangular periodic substrates is investigated using Langevin dynamical simulations. When the lattice structure of the…
We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky(ST). The simulation starts from the…
We study the spontaneous motion, binary collisions, and collective dynamics of "polar disks", i.e. purpose-built particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their…
We consider a system of $N$ bosons interacting in a three-dimensional box endowed with periodic boundary condition that is strongly confined in one direction such that the normalized thickness of the box $d\ll1$. We assume particles to…
The motion of tiny heavy particles transported in a co-rotating vortex pair, with or without particle inertia and sedimentation, is investigated. The dynamics of non-inertial sedimenting particles is shown to be chaotic, under the combined…
This study analyzes the Collatz map through nonlinear dynamics. By embedding integers in Sharkovsky's ordering, we show that odd initial values suffice for full dynamical characterization. We introduce ``direction phases'' to partition…
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…