Related papers: Infinite-volume mixing for dynamical systems prese…

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…

Mixability is a property of a loss which characterizes when fast convergence is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the exp and log operations present in the…

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a…

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…

This book chapter introduces to the concept of weak chaos, aspects of its ergodic theory description, and properties of the anomalous dynamics associated with it. In the first half of the chapter we study simple one-dimensional…

We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in $\mathbb{R}^d$, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is…

How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…

Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…

In equilibrium systems, the conservation of the number of particles (or mass) leads to the equalization of the chemical potential throughout the system. Using a non-equilibrium generalization of the notion of chemical potential, we…

Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…

The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…

We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic…

We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant…

We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an…

Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to…

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…

Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the…

For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We…

The theory of dissipativity has been primarily developed for controllable systems/behaviors. For various reasons, in the context of uncontrollable systems/behaviors, a more appropriate definition of dissipativity is in terms of the…

Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…