Related papers: Complexities of differentiable dynamical systems

There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…

We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…

This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…

We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…

Uncertainty is an important feature of dynamic systems, and entropy has been widely used to measure this attribute. In this Letter, we prove that state aggregation and decomposition can decrease and increase the entropy, respectively, of…

We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…

In this article a definition of reversible processes in terms of differences in intensive Thermodynamics properties (Affinities) is proposed. This definition makes it possible to both define reversible processes before introducing the…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is extended to sociology or economics. Diversity can be intended as the count of different items, animals, or, more generally, interactions. There are two…

Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…

Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic…

In these notes we review emergent phenomena in complex systems, emphasizing ways to identify potential underlying universal mechanisms that generates complexity. The discussion is centered around the emergence of collective behavior in…

It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$…

We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…

We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of…

The present article introduces a reference framework for discussing resilience of computational systems. Rather than a property that may or may not be exhibited by a system, resilience is interpreted here as the emerging result of a dynamic…

From bird flocking to neural dynamics, complex systems generate fascinating structures and correlations. Often, seemingly simple dynamics lead to intricate emergent properties. Despite their visceral appeal, defining complex systems lacks…

A mathematical interpretation of the usual definition of entropy (for a discrete probability distribution or a trace 1 positive operator) is given. This formulation makes some properties of entropy immediate.

This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…