Related papers: Melnikov method for autonomous Hamiltonians
The Melnikov method is applied to a class of generalized Ziegler pendulums. We find an analytical form for the separatrix of the system in terms of Jacobian elliptic integrals, holding for a large class of initial conditions and parameters.…
Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov…
We illustrate a completely analytic approach to Mel'nikov theory, which is based on a suitable extension of a classical method, and which is parallel and -- at least in part -- complementary to the standard procedure. This approach can be…
In this work the Melnikov method for perturbed Hamiltonian wave equations is considered in order to determine possible chaotic behaviour in the systems. The backbone of the analysis is the multi-symplectic formulation of the unperturbed PDE…
The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply the Mielnik's construction in supersymmetric…
A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can find a unitary transformation such that the transformed quadratic Hamiltonian is diagonal but still written in terms of the original position and…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
We consider Arnoldi like processes to obtain symplectic subspaces for Hamiltonian systems. Large systems are locally approximated by ones living in low dimensional subspaces; we especially consider Krylov subspaces and some extensions. This…
The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…
In this paper, we propose integrable discretizations of a two-dimensional Hamiltonian system with quartic potentials. Using either the method of separation of variables or the method based on bilinear forms, we construct the corresponding…
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
This paper is dedicated to clarifying and introducing the correct application of Melnikov method in fractional dynamics. Attention to the complex dynamics of hyperbolic orbits and to fractional calculus can be, respectively, traced back to…
In a recent paper by the author (K. Yagasaki, Nonintegrability of the restricted three-body problem, submitted for publication), a technique was developed for determining whether nearly integrable systems are not meromorphically…
We develop a Melnikov framework for the Kuramoto Sivashinsky (KS) equation under weak deterministic and stochastic forcing. By treating KS as an infinite dimensional dynamical system, we derive a Melnikov functional that measures splitting…
We continue a previous paper to show that Mel'nikov's first order formula for part of the separatrix splitting of a pendulum under fast quasi periodic forcing holds, in special examples, as an asymptotic formula in the forcing rapidity.
In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold $x=0$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the…
We consider the question of existence of Hamiltonians for autonomous non-holonomic mechanical systems in this paper. The approach is elementary in the sense that the existence of a Hamiltonian for a given non-holonomic system is considered…
A general method to construct basis functions for fermionic systems which account for the $SU(2)$ symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system…
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
The Mishenko-Fomenko theorem on action-angle coordinates for superintegrable autonomous Hamiltonian systems is extended to the non-autonomous ones.