Related papers: On Dynamical System and Topological Transitivity v…
The stable critical points and their corresponding cosmology are derived in the teleparallel gravity with an added Gauss-Bonnet topological invariant term. We have analyzed the dynamics of the Universe by presenting two cosmological viable…
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
Let $T\times X\rightarrow X, (t,x)\mapsto tx$, be a topological semiflow on a topological space $X$ with phase semigroup $T$. We introduce and discuss in this paper various transitivity dynamics of $(T,X)$.
We propose a relaxation to the definition of well-structured transition systems (\WSTS) while retaining the decidability of boundedness and non-termination. In this class, the well-quasi-ordered (wqo) condition is relaxed such that it is…
We establish that solving an optimal transportation problem in which the source and target densities are defined on manifolds with different dimensions, is equivalent to solving a new nonlocal analog of the Monge-Amp\`ere equation,…
This paper studies a system of $m$ variational inequalities with interconnected obstacles in infinite horizon associated to optimal multi-modes switching problems. Our main result is the existence and uniqueness of a continuous solution in…
We study the topological entropy of hom tree-shifts and show that, although the topological entropy is not a conjugacy invariant for tree-shifts in general, it remains invariant for hom tree higher block shifts. In…
This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…
This paper explores transverse coordinates for the purpose of orbitally stabilizing periodic motions of nonlinear, control-affine dynamical systems. It is shown that the dynamics of any (minimal or excessive) set of transverse coordinates,…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We take the first steps towards a better understanding of continuous orbit equivalence, i.e., topological orbit equivalence with continuous cocycles. First, we characterise continuous orbit equivalence in terms of isomorphisms of C*-crossed…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a…
Given a dynamical system $(X,T)$ and a family $\mathsf{I}\subseteq \mathcal{P}(\omega)$ of "small" sets of nonnegative integers, a point $x \in X$ is said to be $\mathsf{I}$-strong universal if for each $y \in X$ there exists a subsequence…
Recently, alternating transition systems are adopted to describe control systems with disturbances and their finite abstract systems. In order to capture the equivalence relation between these systems, a notion of alternating approximate…
A derivation of the "exact" two-point equations analogous to those used as a basis for one-point Reynolds-Averaged Navier-Stokes turbulence model for variable density, incompressible turbulence. The purpose is to present the statistical…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…
In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated…