Related papers: A completion construction for continuous dynamical…

In this paper, we derive a number of interesting properties and extensions of the convex flow problem from the perspective of convex geometry. We show that the sets of allowable flows always can be imbued with a downward closure property,…

Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown's formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a…

We consider discrete dynamical systems whose phase spaces are compact metrizable countable spaces. In the first part of the article, we study some properties that guarantee the continuity of all functions of the corresponding Ellis…

The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…

Flows on surfaces are one of the most fundamental and classical objects in dynamical systems, and are studied from various areas (e.g. integrable systems, differential equations, fluid mechanics). Though hyperbolic flows and recurrent flows…

In the article "Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane" we constructed a compact topological space for the combinatorics of "A regular pentagonal tiling of the plane", which we…

If $N \subset \R$ is a separable II$_1$-factor, the space $\Hom(N,\R)$ of unitary equivalence classes of unital *-homomorphisms $N \to \R$ is shown to have a surprisingly rich structure. If $N$ is not hyperfinite, $\Hom(N,\R)$ is an…

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…

Let $M$ be a compact manifold equipped with a pair of complementary foliations, say horizontal $\mathcal{H}$ and vertical $\mathcal{V}$. In Melo, Morgado and Ruffino (Disc Cont Dyn Syst B, 2016, 21(9)) it is proved that if a semimartingale…

Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…

This paper studies various completeness properties of the open-point and bi-point-open topologies on the space C(X) of all real-valued continuous functions on a Tychonoff space X. The properties range from complete metrizability to the…

Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate…

In this paper, we construct a geometrical compactification of the geodesic flow of non-compact complete hyperbolic surfaces $\Sigma$ without cusps having finitely generated fundamental group. We study the dynamical properties of the…

The relationship of network structure and dynamics is one of most extensively investigated problems in the theory of complex systems of the last years. Understanding this relationship is of relevance to a range of disciplines -- from…

Existence of random dynamical systems for a class of coalescing stochastic flows on $\mathbb{R}$ is proved. A new state space for coalescing flows is built. As particular cases coalescing flows of solutions to stochastic differential…

Our interest in this work is in group extensions of minimal flows with compact abelian groups in the fibres. We study their structure from categorical and algebraic points of view, and describe relations of their dynamics to the…

Constructal Law states that a finite-size flow system that persists in time evolves its configuration so as to provide progressively easier access to the currents that flow through it. Classical Constructal theory derives hierarchical flow…

Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…

We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…

We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In…