Related papers: Variational principle for the determination of uns…
We present a new formulation to construct numerically equilibrium configurations of rotating stars in general relativity. Having in mind the application to their quasi static evolutions, we adopt a Lagrangian formulation of our own…
We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…
In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…
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…
This study investigates the problem of areostationary orbits around Mars in the three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no…
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle:…
We consider invariant matrix models with log-normal (asymptotic) weight. It is known that their eigenvalue distribution is intermediate between Wigner-Dyson and Poissonian, which candidates these models for describing a system intermediate…
The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems,…
We numerically solve the underdamped Langevin equation to obtain the trajectories of a particle in a sinusoidal potential driven by a temporally sinusoidal force in a medium with coefficient of friction periodic in space as the potential…
In this expository article we study the question of the existence of periodic orbits of prescribed energy for classical Hamiltonian systems on compact configuration spaces. We use a variational approach, by studying how the behavior of the…
A Lagrangian system with two degrees of freedom is considered. The configuration space of the system is a cylinder. A large class of periodic solutions has been found. The solutions are not homotopy equivalent to each other.
We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and…
Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas of dynamical systems. A popular version of the LDs consists in computing the arc-length of trajectories over a…
Motivated by the possibility of radiation driven instabilities in rotating magnetic stars, we study the stability properties of general linear perturbations of a stationary and axisymmetric, infinitely conducting perfect fluid configuration…
Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of…
Advances in the variational approach to the $n$-body problem have led to significant progress in celestial mechanics, uncovering new types of possible orbits. In this paper, critical points of the Lagrangian action associated with the…
We investigate the existence and properties of equipotential surfaces and Lagrangian points in non-synchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…