Related papers: Fractal trajectories of the dynamical system
We study non-equilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state…
We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, which are of particular…
Scaling properties of Yang-Mills fields are used to show that fractal structures are expected to be present in system described by those theories. We show that the fractal structure leads to recurrence formulas that allow the determination…
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119,…
A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such fractal. Its Haussdorf dimension and…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
In this work, with the help of fractional calculus, it is shown a time dependence of entropy more general than the well known Pesin relation is derived. Here the equiprobability postulate is not assumed, the system dynamic in the phase…
A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
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…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
Transport by normal diffusion can be decomposed into the so-called hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structure of these hydrodynamic…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…