Related papers: The shadowing property for piecewise monotone inte…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
For a continuous self-map of a compact metric space, we provide a sufficient condition for the orbit of a point to converge to a periodic orbit or an odometer. We show that if a continuous self-map of a compact metric space has the…
The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of…
In this paper, we introduce the concept of S-expansiveness for local homeomorphisms and demonstrate that a class of extended symbolic dynamics, known as zip shift maps, are S-expansive and possess the shadowing property. Furthermore, we…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we show that a broad class of real-analytic deformations of…
We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The dynamics of the phase transition of the continuum $\Phi ^{4}_{1+1}$-theory in Light Cone Quantization is reexamined taking into account fluctuations of the order parameter $< \Phi >$ in the form of dynamical zero mode operators (DZMO)…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
We reflect on the possibility of having a matter action that is invariant only under transverse diffeomorphisms. This possibility is particularly interesting for the dark sector, where no restrictions arise based on the weak equivalence…
General features of the $\alpha-\beta$ transition of quartz are investigated. Molecular dynamics methods are mainly used, an analytic treatment being deferred to a work in preparation. A basic preliminary observation is that the transition…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
Trace Dynamics is a classical dynamical theory of noncommuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a…
Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…