相关论文: The 1:1 resonance in Hamiltonian systems
In this paper, we investigate wave scattering by a pair of closely spaced inclusions embedded in a homogeneous medium, characterized by a high contrast physical parameters. The system is modeled by the two-dimensional Helmholtz equation. We…
A wide class of Hamiltonian systems with N degrees of freedom and endowed with, at least, (N-2) functionally independent integrals of motion in involution is constructed by making use of the two-photon Lie-Poisson coalgebra. The set of…
Motivated by the population of multi-planet systems with orbital period ratios 1<P2/P1<2, we study the long-term stability of packed two planet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits…
An approximate Poincare map near equally strong multiple resonances is reduced by means the method of averaging. Near the resonance junction of three degrees of freedom, we find that some homoclinic orbits ``whiskers'' in single resonance…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We consider the break-up of invariant tori in Hamiltonian systems with two degrees of freedom with a frequency which belongs to a cubic field. We define and construct renormalization-group transformations in order to determine the threshold…
We give an account of the various changes in the stability character in the five types of Riemann ellipsoids by establishing the occurrence of different quasi-periodic Hamiltonian bifurcations. Suitable symplectic changes of coordinates,…
In this paper, we present a model describing the time evolution of two dimensional surface waves in gravity and infinite depth. The model of six interacting modes derives from the normal form of the system describing the dynamics of surface…
Overlapping resonances are shown to provide new insights into the extent of decoherence experienced by a system superposition state in the regime of strong system- environment coupling. As an example of this general approach, a generic…
Multi-frequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated using a complex Ginzburg-Landau equation that systematically captures weak forcing functions that simultaneously hit the…
Our main result is the complete set of explicit conditions necessary and sufficient for isochronicity of a Hamiltonian system with one degree of freedom. The conditions are presented in terms of Taylor coefficients of the Hamiltonian…
The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
We investigate conformal relative equilibria for Hamiltonian systems on exact Poisson manifolds equipped with scaling symmetries. By introducing conformally Poisson actions and conformal momentum maps, we characterize these equilibria…
In this paper we are concerned with the periodic Hamiltonian system with one degree of freedom, where the origin is a trivial solution. We assume that the corresponding linearized system at the origin is elliptic, and the characteristic…
We investigate an analytical treatment of bifurcations of families of resonant `thin' tubes in axisymmetric galactic potentials. We verify that the most relevant bifurcations are due to the (1:1) resonance producing the `inclined' orbits…
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the…
In high dimensions, reflective Hamiltonian Monte Carlo with inexact reflections exhibits slow mixing when the particle ensemble is initialised from a Dirac delta distribution and the uniform distribution is targeted. By quantifying the…
We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate $1:1$ or $1:-1$ semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite…