Related papers: Periodic orbits in the logarithmic potential
We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct…
Higher precision efficient computation of period 1 relaxation oscillations of strongly nonlinear and singularly perturbed Rayleigh equations with external periodic forcing is presented. The computations are performed in the context of…
Let $f:M\to M$ be a $C^{1+\epsilon}$-map on a smooth Riemannian manifold $M$ and let $\Lambda\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic…
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…
In exploratory factor analysis, rotation techniques are employed to derive interpretable factor loading matrices. Factor rotations deal with equality-constrained optimization problems aimed at determining a loading matrix based on measure…
We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions…
It is often assumed that a warped galaxy can be modeled by a set of rings. This paper verifies numerically the validity of this assumption by the study of periodic orbits populating a heavy self-gravitating warped disk. The phase space…
A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for…
We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
We show how a variant of the Lefschetz Fixed Point Theorem may be used to count the number of periodic orbits for certain rational difference equations.
This paper explores orbits in extended mass distributions and develops an analytic approximation scheme based on epicycloids (spirograph patterns). We focus on the Hernquist potential which provides a good model for many astrophysical…
In this paper, we overlay a continuum of analytical relations which essentially serve to compute the arc-length described by a celestial body in an elliptic orbit within a stipulated time interval. The formalism is based upon a…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…
In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited…