Related papers: Two-dimensional dynamical systems admitting the no…

We provide a relation which describes how the entanglement of two d-level systems evolves as either system undergoes an arbitrary physical process. The dynamics of the entanglement turns out to be of a simple form, and is fully captured by…

A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are…

We explore the properties of physical theories in space-times with two time dimensions. We show that the common arguments used to rule such theories out do not apply if the dynamics associated with the additional time dimension is thermal…

Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…

Two-time physics (2T) is a general reformulation of one-time physics (1T) that displays previously unnoticed hidden symmetries in 1T dynamical systems and establishes previously unknown duality type relations among them. This may play a…

Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…

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…

The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…

We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically…

Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in…

The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…

We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…

The distinct models that describe spin 1 and 2 massive excitations in 2+1 dimensions are analized, showing their equivalence (between models of same spin) and analogies (between models of different spin). Topics as spontaneous symmetry…

The problem of metrizability for the dynamical systems accepting the normal shift is formulated and solved. The explicit formula for the force field of metrizable Newtonian dynamical system $\ddot\bold r=\bold F(\bold r,\dot\bold r)$ is…

We consider two types of dynamical systems namely non-autonomous discrete dynamical systems(NDDS) and generic dynamical systems(GDS). In both of them, we study various notions of transitivity. We give many equivalent conditions for each of…

We investigate the switching dynamics of multistable nematic liquid crystal devices. In particular we identify a remarkably simple 2-dimensional (2D) device which exploits hybrid alignment at the surfaces to yield a bistable response. We…

In this work, we study the nature of transitions between inherent structures of a two-dimensional model supercooled liquid. We demonstrate that these transitions occur predominately along a small number of directions on the energy…

We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and…

A primitive type of two-dimensional dynamic system is introduced. It is shown that there is no decision procedure able to answer if such a dynamical system is ultimately zero.

We investigate the dynamical coupling between the motion and the deformation of a single self-propelled domain based on two different model systems in two dimensions. One is represented by the set of ordinary differential equations for the…