Related papers: Chaotic weighted shifts on directed trees
In a recent paper [15], Hilbert space operators $T$ with the property that each sequence of the form $\{\|T^n h\|^2\}_{n=0}^{\infty}$ is conditionally positive definite in a semigroup sense were introduced. In the present paper, this line…
In this paper, we characterize supercyclic weighted composition operators on a large class of solid Banach function spaces, in particular on Lebesgue, Orlicz and Morrey spaces. Also, we characterize supercyclic weighted composition…
Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…
We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w,\varphi}$ on Banach spaces of analytic functions on the unit disk $\mathbb{D}$. Under natural conditions on the space, we show that $C_{w,\varphi}$ is…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
We study the effects of animal social networks with a weighted pattern of interactions on the flocking transition exhibited by models of self-organized collective motion. Considering a model representing dynamics on a one-dimensional…
For any continuous self-map of a compact metric space, we prove a saturation of distributionally scrambled Mycielski sets under a type of shadowing and the chain transitivity.
In this paper, we characterize mixing unilateral backward shifts on barrelled and ultrabarrelled topological sequence spaces respectively, which extend several well-known results in the existing literature. We present some nontrivial…
The dynamics of the left translation semigroup $\{T_t\}_{t \geq 0}$ on weighted $L^p$ spaces over a directed metric tree $L(G)$ is investigated. Necessary and sufficient conditions on the weight family $\rho$ for the strong continuity of…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
In this paper, we study the hypercyclic composition operators on weighted Banach spaces of functions defined on discrete metric spaces. We show that the only such composition operators act on the "little" spaces. We characterize the bounded…
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…
We consider weighted composition operators, that is operators of the type $g \mapsto w \cdot g \circ f$, acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition…
This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the dynamical system is densely uniformly Li-Yorke chaotic. It…
We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded…
We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models.…
We characterize the strictly increasing symbols $\varphi:\mathbb{N}_0\longrightarrow\mathbb{N}_0$ whose composition operators $C_{\varphi}$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space…
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…
Recurrence networks are powerful tools used effectively in the nonlinear analysis of time series data. The analysis in this context is done mostly with unweighted and undirected complex networks constructed with specific criteria from the…