Related papers: Dynamical systems on chain complexes and canonical…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
In this article, we present a landing theorem for periodic dynamic rays for transcendental entire maps which have bounded post-singular sets, by using standard hyperbolic geometry results.
We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss…
Some subjects related to the geometric theory of singular dynamical systems are reviewed in this paper. In particular, the following two matters are considered: the theory of canonical transformations for presymplectic Hamiltonian systems,…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
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…
Identifying the dynamic precompensator that renders a nonlinear control system feedback linearizable is a challenging problem. Researchers have explored the problem -- dynamic feedback linearization -- and produced existence conditions and…
We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.
Several studies analyzed certain nonlinear dynamical systems by showing that the cyclic number of sign variations in the vector of derivatives is an integer-valued Lyapunov function. These results are based on direct analysis of the…
Using a non-perturbative classical approach, we study the dynamics of a mobile particle interacting with an infinite one-dimensional (1D) chain of harmonic oscillators. This minimal system is an effective model for many 1D transport…
The paper deals with a dynamical system analysis related to phantom cosmological model . Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
We consider extensions of the notion of topological transitivity for a dynamical system $(X,f)$. In addition to chain transitivity, we define strong chain transitivity and vague transitivity. Associated with each there is a notion of…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers and $\O$ be its integral ring. The convergent power series with coefficients in $\O$ are studied as dynamical systems on $\O$. A minimal decomposition theorem for…
The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…
It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
The virial theorem is established in the framework of resolution-scale relativity for stochastic dynamics characterized by a diffusion constant D. It only relies on a simple time average just like the classical virial theorem, while the…