Related papers: Understanding complex dynamics by means of an asso…
Many real-analytic flows, e.g. in chemical kinetics, share a multiple time scale spectral structure. The trajectories of the corresponding dynamical systems are observed to bundle near so-called slow invariant manifolds (SIMs), which are…
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…
Dynamical tide consists of various waves that can resonate with orbital motion. We test this coupling of dynamical tide and orbital motion using a simple two-dimensional shallow water model, which can be applied to a rocky planet covered…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
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…
We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…
In the mathematical framework of a restricted, slightly dissipative spin-orbit model, we prove the existence of periodic orbits for astronomical parameter values corresponding to all satellites of the Solar system observed in exact…
Quantum mechanics is able to predict challenging behaviors even in the simplest physical scenarios. These behaviors are possible because of the important dynamical role that phase plays in the evolution of quantum systems, and are very…
Periodic orbits (equivalence classes of closed paths up to cyclic shifts) play an important role in applications of graph theory. For example, they appear in the definition of the Ihara zeta function and exact trace formulae for the spectra…
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we…
In this work, we uncover a layered organization of the state space in the Kuramoto-Sivashinsky equation with periodic boundary conditions, in which multiple invariant sets coexist at fixed system parameters and are selected by the initial…
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatio-temporal systems including fluid turbulence is supported by non-chaotic, exactly recurring time-periodic solutions of the…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
First principles should predetermine physical geometry and dynamics both together. In the "algebrodynamics" they follow solely from the properties of the biquaternion algebra $\B$ and the analysis over $\B$. We briefly present the…
In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe…
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of…
We extend the definition of an orbit portrait to the context of non-autonomous iteration, both for the combinatorial version involving collections of angles and for the dynamic version involving external rays where combinatorial portraits…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
We consider the dynamical behavior of Martin-L\"of random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic…