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We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
Graph databases in many applications---semantic web, transport or biological networks among others---are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries…
Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb{R}^{d})$ called a potential we define its rotation set $R(F)$ as the set of integrals of $F$ with respect to all $T$-invariant…
We study genericity of dynamical properties in the space of homeomorphisms of the Cantor set and in the space of subshifts of a suitably large shift space. These rather different settings are related by a Glasner-King type correspondence:…
In this paper we study the general concept of integrability in the broad sense within the frame of differential Galois theory. We concentrate on the gradient systems which are not integrable. In spite of it, if we consider them as the real…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Our first goal in this work is to study general and model-independent properties of cyclic cosmologies. The large number of studies of bouncing cosmologies and different cyclic scenarios published recently calls for a proper understanding…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
It is known that the time evolution of a subsystem from an initial state to two later times, t1, t2 (t2 > t1), are both completely positive (CP) but it is shown here that in the intermediate times between t1 and t2, in general, it need not…
The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a…
Recent works have revealed that matching conditions play a major role on general consistency properties of relativistic fluid dynamics such as causality, stability and wellposedness of the equations of motion. In this paper we derive…
Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
We explore developing rich semantic models of systems. Specifically, we consider structured causal explanations about state changes in those systems. Essentially, we are developing process-based dynamic knowledge graphs. As an example, we…
The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examinining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic…
Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using…
It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2…
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…
The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In…