Related papers: Integrals and chaos in generalized H\'{e}non-Heile…
In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…
We show the existence of drifting orbits for certain perturbations of non-convex Hamiltonian systems with several degrees of freedom. These orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes…
The Hamiltonian Theory of the fractional quantum Hall (FQH) regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this paper we include disorder in our treatment, and show…
Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic case is well-established, very few…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
The transition from rotational to discontinuous behavior of the return map of the perturbed oscillators-step system, a paradigm model for a perturbation of a pseudo-integrable Hamiltonian impact system, is studied. The form of the return…
In this paper we study the dynamics near the equilibrium point of a family of Hamiltonian systems in the neighborhood of a $0^2 iw$ resonance. The existence of a family of periodic orbits surrounding the equilibrium is well-known and we…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
We show that a large class of physical theories which has been under intensive investigation recently, share the same geometric features in their Hamiltonian formulation. These dynamical systems range from harmonic oscillations to WZW-like…
We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamilto-nian, we estimate the size of the…
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian…
We define the general Hill system and briefly analyze its dynamical behavior. A particular Hill system representing the interaction of a Keplerian binary system with a normally incident circularly polarized gravitational wave is discussed…
The holomorphic multiplicative chaos (HMC) is a holomorphic analogue of the Gaussian multiplicative chaos. It arises naturally as the limit in large matrix size of the characteristic polynomial of Haar unitary, and more generally…
The motion of a particle near the RN black hole horizon is described by conformal mechanics. Models of this type have no ground state with vanishing energy. This problem was resolved in past by a redefinition of the Hamiltonian which breaks…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
We present a comparison of different numerical techniques for the integration of variational equations. The methods presented can be applied to any autonomous Hamiltonian system whose kinetic energy is quadratic in the generalized momenta,…
This paper summarises a numerical investigation which aimed to identify and characterise regular and chaotic behaviour in time-dependent Hamiltonians H(r,p,t) = p^2/2 + U(r,t), with U=R(t)V(r) or U=V[R(t)r], where V(r) is a polynomial in x,…
We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between…
We study the integrability of a two-dimensional Hamiltonian system with a gyroscopic term and a non-homogeneous potential composed of two homogeneous components of different degrees. The model describes the motion of a particle in a plane…