Related papers: Discrete Dynamical Systems From Real Valued Mutati…

We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…

We have researched the condition for symplectic discretization to preserve local boundedness for the space of 2-dimensional Hamiltonian dynamical systems in this paper.

We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an…

We show that the asymptotic behavior of the two main competing notions of rank of a linear series on a tropical curve is governed by asymptotic invariants, closely paralleling the theory of volumes in algebraic geometry. We introduce and…

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…

To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

We give an autoequivalence of the derived category of the Ginzburg dg algebra for a mutation loop satisfying the sign stability introduced in [IK21]. We compute the categorical entropies of their restrictions to some subcategories and…

We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…

This paper studies a dynamical system, which contains two contours. There is a cluster on each contour. The cluster contains particles, located in adjacent cells. The clusters move under prescribed rules. The delays of clusters are due to…

Studies of periodically driven one-dimensional many-body systems have advanced our understanding of complex systems and stimulated promising developments in quantum simulation. It is hence of interest to go one step further, by…

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…

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 consider a prototypical two-parameter family of invertible maps of $\mathbb{Z}^2$, representing rotations with decreasing rotation number. These maps describe the dynamics inside the island chains of a piecewise affine discrete twist map…

We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by applying round-off to planar rotations. All orbits of these maps are conjectured to be periodic. We let the angle of rotation approach pi/2, and…

Dynamists have been studying Hamiltonian systems for a long time. However, many physical systems are dissipative and do not preserve a symplectic form. This is the case, for example, with systems involving friction, which multiply the…

We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This…

Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…

The dynamics of a close binary system of globular clusters is considered. It is shown that the star transfer process from one of the components to the other should lead to the decrease of dimension of the first cluster with simultaneous…

In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a…