相关论文: Arithmetic Dynamics
In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain geometric meaning of basic invariants of vector distributions.
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
In this paper, the intuitive idea of tilt is formalised into the rigorous concept of tilt rotations. This is motivated by the high relevance that pure tilt rotations have in the analysis of balancing bodies in 3D, and their applicability to…
Dynamical theories of speech use computational models of articulatory control to generate quantitative predictions and advance understanding of speech dynamics. The addition of a nonlinear restoring force to task dynamic models is a…
We study arithmetic degree of a dominant rational self-map on a smooth projective variety over a function field of characteristic zero. We see that the notion of arithmetic degree and some related problems over function fields are…
Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…
The main directions in the development of the nonholonomic dynamics are briefly considered in this paper. The first direction is connected with the general formalizm of the equations of dynamics that differs from the Lagrangian and…
Given a totally finite ordered alphabet $ A $, endowing the set of words over $ A $ with the alternating lexicographic order, we define a new class of Lyndon words. We study the fundamental properties of the associated symbolic dynamical…
In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive characteristic. We generalise some basic facts on arithmetic degree and canonical height in positive characteristic. As applications, we…
The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoveries and recent developments on the Herman ring of rational and…
We construct a piecewise onto 3-to-1 dynamical system on the positive quadrant of the unit circle, such that for rational points (which correspond to normalized Primitive Pythagorean Triples), the associated ternary expansion is finite, and…
For minimal $\mathbb{Z}^{2}$-topological dynamical systems, we introduce a cube structure and a variation of the regionally proximal relation for $\mathbb{Z}^2$ actions, which allow us to characterize product systems and their factors. We…
In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…