On merging of resonant periodic orbits 4:3; 3:2 and 2:1 in Sun-Jupiter photo gravitational restricted three-body problem

We explore the merging of resonant periodic orbits in the frame work of planar circular restricted three body problem with the help of Poincaré surface of section. We have studied the effect of solar radiation pressure on 4:3, 3:2 and 2:1 periodic orbits. It is found that radiation pressure helps in merging these orbits (4:3 and 3.2 into 1:1 resonance and 2:1 into 1:1 resonance). At the time of merging these orbits become near-circular. The period and size of these orbits reduce with the increase in radiation pressure.

A REVIEW STUDY OF THE 3-PARTICLE TODA LATTICE AND HIGHER ORDER TRUNCATIONS: THE EVEN-ORDER CASES — PART II

We complete the study of the numerical behavior of the truncated 3-particle Toda lattice (3pTL) with even truncations at orders n = 2k, k = 2, …, 10. We use (as in Part I): (a) the method of Poincaré surface of section, (b) the maximum Lyapunov characteristic number and (c) the ratio of the families of ordered periodic orbits. We derived some similarities and quite many differences between the odd and even order expansions.

A REVIEW STUDY OF THE 3-PARTICLE TODA LATTICE AND HIGHER-ORDER TRUNCATIONS: THE ODD-ORDER CASES — PART I

The numerical behavior of the truncated 3-particle Toda lattice (3pTL) is reviewed and studied in more detail (than in previous papers) and at higher energies (at odd-orders n ≤ 9). We further extended our study to higher truncations at odd-orders, n = 2k + 1, k = 1, …, 9. We have located the majority of the families of periodic orbits along with their main bifurcations. By using: (a) the method of Poincaré surface of section, (b) the maximum Lyapunov characteristic number and (c) the ratio of the families of ordered periodic orbits, we studied the topology of the nine odd-order Hamiltonians with respect to their order of truncation.

Stability of an electron beam in a two-frequency wiggler with a self-generated field

We investigate the relativistic electron motions in a two-frequency wiggler magnetic field with self-generated fields. The equations of motion are derived from the Hamiltonian which include the self-generated field, and we find the steady-state orbit from the equations of motion. The stability of electron motion in a two-frequency wiggler is examined by the numerical simulation. We analyze the a dynamical systems using the fast Fourier transformation and the Poincarè surface of section to find the critical value which have the periodical electron motion and to optimize the two-frequency wiggler.

Collision and Stable Regions around Bodies with Simple Geometric Shape

We show the expressions of the gravitational potential of homogeneous bodies with well-defined simple geometric shapes to study the phase space of trajectories around these bodies. The potentials of the rectangular and triangular plates are presented. With these expressions we study the phase space of trajectories of a point of mass around the plates, using the Poincaré surface of section technique. We determined the location and the size of the stable and collision regions in the phase space, and the identification of some resonances. This work is the first and an important step for others studies, considering 3D bodies. The study of the behavior of a point of mass orbiting around these plates (2D), near their corners, can be used as a parameter to understand the influence of the gravitational potential when the particle is close to an irregular surface, such as large craters and ridges.

CHAOS IN ABELIAN AND NON-ABELIAN HIGGS SYSTEMS

The nonintegrability and chaotic nature of the Yang-Mills Higgs systems are considered. We have studied the Abelian Higgs model and the SO(3) Georgi-Glashow model (non-Abelian Higgs model), which possess vortices and monopole solutions respectively. The Painlevé analysis of the corresponding time-dependent equations of motion shows that both systems are nonintegrable for all choices of the parameter values. The Poincare surface-of-section plot shows the presence of chaotic trajectories in the phase space at certain parameter values for both systems. The chaotic nature of the trajectories is also indicated by the computations of the Lyapunov exponents of the corresponding systems.