Related papers: Neumann system and hyperelliptic al functions

Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly…

We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties,…

We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…

This is a survey on finite-dimensional integrable dynamical systems related to Hamiltonian $G$-actions. Within a framework of noncommutative integrability we study integrability of $G$-invariant systems, collective motions and reduced…

This study introduces standard Cliffordian Kaehler analogue of Hamiltonian mechanic systems. In the end, the some results related to standard Cliffordian Kaehler dynamical systems are also discussed.

A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as…

In the previous article (J. Geom. Phys. {\bf 43} (2002) 146), we show the hyperelliptic solutions of a loop soliton as a study of a quantized elastica. This article gives some functional relations in a loop soliton as a quantized elastica.

In the mean-field regime, we prove convergence (with explicit bounds) of the many-body von Neumann dynamics with bounded interactions to the Hartree-von Neumann dynamics.

Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in a Grassmann algebra with two generators. The equations of motion are explicitly…

We propose a simple density functional expression for the upper bound of the kinetic energy for electronic systems. Such a functional is valid in the limit of slowly varying density, its validity outside this regime is discussed by making a…

In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…

In a previous paper [3] we have studied flows defined on polytopes, presenting a new method to encapsulate its asymptotic dynamics along the edge-vertex heteroclinic network. These results apply to the class of polymatrix replicator…

This survey gives a unified treatment of topics from Abelian and non-Abelian Nielsen Theory integrated with the semiconjugacy theorems of Franks and Handel. The main focus is to develop an analog of the rotation set that is valid when the…

We investigate the notion of H-subdifferential and H-normal map of a function on the Heisenberg group, based on its sub-Riemannian structure. In particular, a characterization of the convexity of a function is given via the nonemptiness of…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

In this paper, we deal with a q-Dirac system. We investigate some spectral properties and the asymptotic behavior of the eigenvalues and the eigenfunctions of this q-Dirac system.

In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the first results which provide classes of…

The action-angle variables for N-particle Hamiltonian system with the Hamiltonian $H=\sum_{n=0}^{N-1} \ln sh^{-2}(p_n/2)+\ln(\wp(x_n-x_{n+1})- \wp(x_n+x_{n+1})), x_N=x_0,$ are constructed, and the system is solved in terms of the Riemann…

By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…

In this paper, we extend the nontangential maximal function estimate obtained by C. Kenig, F. Lin and Z. Shen in \cite{KFS1} to the nonhomogeneous elliptic operators with rapidly oscillating periodic coefficients. The result relies on the…