相关论文: Analytical Expression for Low-dimensional Resonanc…

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…

Analytical periodic solutions for weakly Coupled Map Lattices are shown in an explicit form as well as in a recurrence relation. The results establish a link between a matricial representation and recurrence relations of the solutions.

We consider (2+1) and (1+1) dimensional long-wave short-wave resonance interaction systems. We construct an extensive set of exact periodic solutions of these systems in terms of Lam\'e polynomials of order one and two. The periodic…

The structure of discrete resonances in water-wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds million) even in comparatively small spectral domain when both scale and angle energy…

The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…

We develop the complex scaling method for the Dirichlet Laplacian in a domain with asymptotically cylindrical end. We define resonances as discrete eigenvalues of non-selfadjoint operators, obtained as deformations of the selfadjoint…

In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when…

We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting of small amplitude. It is well known that such a perturbation does not create eigenvalues…

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.

Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…

n a number of papers it was shown that there are one-dimensional systems such that they contain solutions with, so called, overcompressive singular shock waves besides the usual elementary waves (shock and rarefaction ones as well as…

We study analytically and experimentally certain symplectic and time-reversible N-body integrators which employ a Kepler solver for each pair-wise interaction, including the method of Hernandez & Bertschinger (2015). Owing to the Kepler…

Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…

We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble.…

Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…

In this paper we study $4$-dimensional affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure $\omega$. We prove that the rank of the shape operator is at most one if…

Fix a compact 4-dimensional manifold with self-dual 2nd Betti number one and with a given symplectic form. This article proves the following: The Frechet space of tamed almost complex structures as defined by the given symplectic form has…

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry…

We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective Hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program…