Related papers: Wielding Intermittency with Cycle Expansions
In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion…
We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer…
In a previous paper, using ergodic theory, Lo [1] derived a simple definite integral that provided an estimate of the view periods of ground stations to satellites. This assumes the satellites are in circular orbits with non-repeating…
We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Using intermittent maps with infinite invariant measures, we investigate the universality of time-averaged observables under aging conditions. According to Aaronson-Darling-Kac theorem, in non-aged dynamical systems with infinite invariant…
The phenomenon of periodic orbit scarring of eigenstates of classically chaotic systems is attracting increasing attention. Scarring is one of the most important "corrections" to the ideal random eigenstates suggested by random matrix…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior of arbitrary order transport moments. The theory is applied to different kinds of one-dimensional intermittent maps, and Lorentz gas with…
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…
We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this method to a wide range of examples, including a…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its…
The chaotic phenomenon of intermittency is modeled by a simple map of the unit interval, the Farey map. The long term dynamical behaviour of a point under iteration of the map is translated into a spin system via symbolic dynamics. Methods…
We apply the averaging theory of high order for computing the limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. These discontinuous piecewise differential systems are formed by two…
We apply periodic-orbit theory to calculate the integrated density of states $N(k)$ from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the results obtained from direct…
We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between…