相关论文: Arithmetic Dynamics
We introduce some tools of symbolic dynamics to study the hyperbolic directions of partially hyperbolic diffeomorphisms, emulating the well known methods available for uniformly hyperbolic systems.
Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…
We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and…
We get three basic results in algebraic dynamics: (1). We give the first algorithm to compute the dynamical degrees to arbitrary precision. (2). We prove that for a family of dominant rational self-maps, the dynamical degrees are lower…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, $\mathcal{U}$-frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and…
Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid…
In this survey we will present the symbolic extension theory in topological dynamics, which was built over the past twenty years.
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of…
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…
We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…