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We introduce a numerical method to integrate tidal effects on collisional systems, using any definition of the external potential as a function of space and time. Rather than using a linearisation of the tidal field, this new method follows…
Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems are geometric analogues of symbolic dynamics. It is…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic…
Birational toggling on Gelfand-Tsetlin patterns appeared first in the study of geometric crystals and geometric Robinson-Schensted-Knuth correspondence. Based on these birational toggle relations, Einstein and Propp introduced a discrete…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
We present an entirely new approach towards a realization of the supersymmetric Yang-Mills theory on the lattice. The action consists of the staggered fermion and the plaquette variables distributed in the Euclidean space with a particular…
We investigate L-sectional curvature of S-manifolds with respect to the Rieman- nian connection and to certain semi-symmetric metric and non-metric connections naturally related with the structure, obtaining conditions for them to be…
This paper does not contain any new results, it is just an attempt to present, in a systematic way, one construction which establishes an interesting relationship between some ideas and notions well-known in the theory of integrable systems…
In this article we propose an algebraic system, which is an abelian group $(A,+)$ with a family of non-associative and non-(left)distributive multiplications $\{\cdot_{\lambda}\}_{\lambda\in H}$. We call this algebraic system dynamical…
Many fundamental structures of Riemannian geometry have found discrete counterparts for graphs or combinatorial ones for simplicial complexes. These include those discussed in this survey, Hodge theory, Morse theory, the spectral theory of…
Two outer automorphisms of infinite-dimensional representations of $sl(2)$ algebra are considered. The similar constructions for the loop algebras and yangians are presented. The corresponding linear and quadratic $R$-brackets include the…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
Tracking Lagrangian coherent structures in dynamical systems is important for many applications such as oceanography and weather prediction. In this paper, we present a collaborative robotic control strategy designed to track stable and…
In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the…
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…
We study the Regge regime of QCD as a special regime of lattice gauge theory on an asymmetric lattice. This lattice has a spacing $a_0 $ in the longitudinal direction and a spacing $a_t $ in the transversal direction. The limit…
In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and…
Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ…