Related papers: On the quantitative dynamical Mordell-Lang conject…

A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

We obtain a complete characterization of all orbits of a quadratic Collatz-type recursion called the divide-or-choose-2 rule. Each orbit either ends in a cycle whose period depends on the initial value or it goes to infinity. We specify…

We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is…

The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…

A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…

We introduce the $k$-variable-occurrence fragment, which is the set of terms having at most $k$ occurrences of variables. We give a sufficient condition for the decidability of the equational theory of the $k$-variable-occurrence fragment…

Entanglement or entanglement generating interactions permit to achieve the maximum allowed speed in the dynamical evolution of a composite system, when the energy resources are distributed among subsystems. The cases of pre-existing…

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.

A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then…

We prove an analogue of the Manin-Mumford conjecture for polynomial dynamical systems over number fields. In our setting the role of torsion points is taken by the small orbit of a point $\alpha$. The small orbit of a point was introduced…

We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise…

Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the…

In this paper, we study multi-rotation orbits on the unit circle. We obtain a natural generalization of a classical result which says that orbits of irrational rotations on the unit circle are dense. It is possible to show that this result…

If a line cuts randomly two sides of a triangle, the length of the segment determined by the points of intersection is also random. The object of this study, applied to a particular case, is to calculate the probability that the length of…

Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…

We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature…

For endomorphisms of projective varieties, we prove that the arithmetic degree of a point with Zariski dense orbit must be a cohomological Lyapunov multiplier of the dynamical system. We will apply our result to deduce a corollary towards…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

We study multiplicative dependence between elements in orbits ofalgebraic dynamical systems over number fields modulo a finitely generated multiplicative subgroup of the field. We obtain a series of results, many of which may be viewed as a…