Related papers: Resonances for homoclinic trapped sets
Migration of planetary systems caused by the action of dissipative forces may lead the planets to be trapped in a resonance. In this work we study the conditions and the dynamics of such resonant trapping. Particularly, we are interested in…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and…
We study small perturbations of a sectional hyperbolic set of a vector field on a compact manifold. Indeed, we obtain robustly finiteness of homoclinic classes on this scenary. Moreover, since attractor and repeller sets are particular…
We consider a forced oscillation and passage through resonance for an infinite-length system, having time-varying parameters and possessing a single trapped mode. The system is a string, lying on the Winkler foundation and equipped with a…
This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…
The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line,…
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-trapping estimates in trapping situations when the resolvent…
High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localisation at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
We generalize some of the results in [arXiv: math.CV/0503430], and prove a bump-lemma for closed sets in semi 1-coronae. From this we obtain some finite cohomology results and an extension theorem for analytic subsets in 1-coronae.
We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To…
We construct $C^2$-robust homoclinic and heterodimensional tangencies of large codimension inside transitive partially hyperbolic sets.