Related papers: The structure of invariant tori in a 3D galactic p…
This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use…
We study the phase space structure and the orbital diffusion from the vicinity of the vertical Lyapunov periodic orbits around the unstable Lagrangian points L1,2 in a 3D barred galaxy model. By perturbing the initial conditions of these…
We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color…
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional…
The investigation of the phase-space properties of structures encountered in a dynamical system is essential for understanding their formation and enhancement. In the present paper we explore the phase space in energy intervals where we…
We investigate how the phase space structure of a 3D autonomous Hamiltonian system evolves across a series of successive 2D and 3D pitchfork and period-doubling bifurcations, as the transition of the parent families of periodic orbits (POs)…
A fundamental premise of Hamiltonian chaos is the existence and properties of tori in phase space. More than a geometrical construct, these structures underlie the very dynamics of both classical and quantal systems. Although presented in…
Owing to the pioneering work of Contopoulos, a strongly barred galaxy is known to have irregular orbits in the vicinity of the bar. By definition, irregular orbits can not be represented by action-angle tori everywhere in phase space. This…
We describe the dynamical behavior of isolated old (> 1 G yr) objects-like Neutron Stars (NSs). These isolated NSs are evolved under smooth, time-independent, 3-D gravitational potentials, axisymmetric and with a triaxial dark halo. We…
We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral…
This study extends the functional perturbation theory~(FPT) of dynamical systems, which was initially developed for investigating the shifts of magnetic field line trajectories within the chaotic edge region of plasma when subjected to…
We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting in a disk, a halo and a bar, to find the origin of boxy components, which are part of the bar or…
A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for…
Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as equilibria, periodic orbits, and invariant tori. This knowledge is significantly increased…
In this article, we consider the dynamics in a neighborhood of a quasi-periodic torus which is invariant by a Hamiltonian flow, we discuss several notions of stability and we prove several results of instability when the frequency of the…
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic dissipative systems; analogous to sums over periodic orbits…
For various values of n, d, and the phase space dimension, we construct simple examples of Hamiltonian and reversible systems possessing smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. In the…
For the case of generic 4D symplectic maps with a mixed phase space we investigate the global organization of regular tori. For this we compute elliptic 1-tori of two coupled standard maps and display them in a 3D phase-space slice. This…
Invariant tori are prominent features of symplectic and volume preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an $n$-dimensional…
Angle-action maps that are periodic in the action direction can have accelerator modes: orbits that are periodic when projected onto the torus, but that lift to unbounded orbits in an action variable. In this paper we construct a…