Related papers: A (short) survey on Dominated Splitting
Hyperbolicity and dominated splitting are two of the most important concepts in the global analysis of differentiable dynamics. In this paper we give several equivalent characterizations of the dominated splitting and in particular we show…
This is a survey on spectral theory of dynamical systems.
We introduce a new notion called generalized dominated splitting which is weaker than classical dominated splitting. We use this notion to generalize a result of Zhang\cite{Zh}: every diffeomorphism with nontrivial global generalized…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
We study domination of quadratic forms in the abstract setting of ordered Hilbert spaces. Our main result gives a characterization in terms of the associated forms. This generalizes and unifies various earlier works. Along the way we…
A stochastic dynamics framework for the study of complex systems is presented.
We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits. Some of the aspects are highlighted in a detailed discussion of a…
This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance". In particular, we show that the limit spectral measure…
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
To make a statement about the nature and mechanism of fragmentation, it is necessary to probe directly any competition, or lack thereof, between the emission of various particle species as a function of excitation energy. The task is then…
Let $\mathcal{S}$ be a dataset of $n$ 2-dimensional points. The top-$k$ dominating query aims to report the $k$ points that dominate the most points in $\mathcal{S}$. A point $p$ dominates a point $q$ iff all coordinates of $p$ are smaller…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.
The concepts of domination and topological index hold great significance within the realm of graph theory. Therefore, it is pertinent to merge these concepts to derive the domination index of a graph. A novel concept of the domination index…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…
In this paper, we study efficient domination in regular graphs.
The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A power dominating set of a graph is a set of vertices from…