Related papers: The generalized Ermakov conservative system: A dis…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
We describe the results that have so far been obtained in the classification problem for integrable (2+1)-dimensional systems of hydrodynamic type. The systems of Gibbons--Tsarev type are the most fundamental here. A whole class of…
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.
A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized…
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra…
Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures,…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
In this work we present new second order semi-discrete central schemes for systems of hyperbolic conservation laws on curvilinear grids. Our methods generalise the two-dimensional central-upwind schemes developed by Kurganov and Tadmor. In…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…
The equations of motion for the variance of strictly one-dimensional or two-dimensional non-relativistic fireballs are derived, from the hydrodynamic equations for an ideal, structureless Boltzmann gas. For this purpose a Gaussian number…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…