Related papers: Periodic orbits in time-dependent planar Stark-Zee…
We present a semi-analytic model atmosphere for close-in exoplanets that captures the essential physics of phase curves: orbital and viewing geometry, advection, and re-radiation. We calibrate the model with the well-characterized…
We consider a charged particle which is driven by a time-dependent flux threading a circular ring system. Various approaches including classical treatment, Fourier expansion method, time-evolution method, and Lewis-Riesenfeld method are…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
The transit time of mean-median orbits ---the time it takes for an orbit to become stationary--- has been conjectured to be finite but unbounded over the rationals. Through a study of some near-regular structures in these orbits, we…
We are interested in stable periodic orbits for spacecrafts in the gravitational field of minor celestial bodies. The stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space…
The strongly interacting system created in ultrarelativistic nuclear collisions behaves almost as an ideal fluid with rich patterns of the velocity field exhibiting strong vortical structure. Vorticity of the fluid, via spin-orbit coupling,…
The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt-angle of…
Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
Periodicities in blazar light curves may be related to helical trajectories in extragalactic radio jets by differential Doppler boosting effects. We consider ballistic and non-ballistic (i.e., radial) trajectories and discuss three possible…
Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that…
We consider a cubic nonlinear wave equation on a network and show that inspecting the normal modes of the graph, we can immediately identify which ones extend into nonlinear periodic orbits. Two main classes of nonlinear periodic orbits…
We consider an autonomous differential system in $\mathbb{R}^n$ with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the…
We have studied the effect of time-dependent ionization and recombination processes on magnetic reconnection in the solar corona. Petschek-type steady reconnection, in which model the magnetic energy is mainly converted at the slow-mode…
We present a new general, complete closed-form solution of the Stark problem in terms of Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our analysis is exact and valid for all values of the…
In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…
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…
Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at…
We present a study of a delay differential equation (DDE) model for the Mid-Pleistocene Transition (MPT). We investigate the behavior of the model when subjected to periodic forcing. The unforced model has a bistable region consisting of a…
We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…