Related papers: Dold sequences, periodic points, and dynamics
The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering…
A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different…
The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We study the quasi-periodicity phenomena occurring at the transition between tonic spiking and bursting activities in exemplary biologically plausible Hodgkin-Huxley type models of individual cells and reduced phenomenological models with…
The long-time behavior is one of the most fundamental properties of dynamical systems. Poincar\'e studied the Poisson stability to capture the property of whether points return arbitrarily near the initial positions. Birkhoff studied the…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
We analyze the relationship between Bott periodicity in topological $K$-theory and the natural periodicity of cyclic homology. This is a basis for understanding the multiplicativity, in odd dimensions, of a bivariant Chern-Connes character…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Dune fields are commonly associated with periodic patterns that are among the most recognizable landscapes on Earth and other planetary bodies. However, in zones of limited sediment supply, where periodic dunes elongate and align in the…
A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized…
We consider the dynamical system created by iterating a morphism of a projective variety defined over the field of fractions of a discrete valuation ring. We study the primitive period of a periodic point in this field in relation to the…
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…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
In this work we construct the $\Co^{\r}$-completion and $\Co^{\l}$-completion of a dynamical system. If $X$ is a flow, we construct canonical maps $X\to \Co^{\r}(X)$ and $X\to \Co^{\l}(X)$ and when these maps are homeomorphism we have the…