相关论文: Attractors and chain recurrence in noncompact spac…
In \cite {kl1}, we extended various notions of recurrence for the generalized semigroup analogous to their counterpart in the classical theory of dynamics. In this paper, we shall address the alternative definition of chain recurrent set in…
It is known by the Conley's theorem that the chain recurrent set $CR(\phi)$ of a deterministic flow $\phi$ on a compact metric space is the complement of the union of sets $B(A)-A$, where $A$ varies over the collection of attractors and…
The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow $\phi$ on the compact metric space $X$, i.e. $X-\mathcal{CR}(\phi)=\bigcup [B(A)-A]$, where…
For a continuous flow on a compact metric space, the aim of this paper is to prove a Conley-type decomposition of the strong chain recurrent set. We first discuss in details the main properties of strong chain recurrent sets. We then…
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper…
We show that attractors are semicontinuous for closed relations on compact Hausdorff spaces. Semicontinuity is what guarantees that small changes to a system do not result in massive growth of certain features, notably attractors. That is,…
In [arXiv:1904.12333], we introduced the concept of escaping set in general setting for a topological space and extended the notion of limit set and escaping set for the general semigroup generated by continuous self maps. In this paper we…
Two types of recurrence sets are introduced for inverse semigroup partial actions in topological spaces. We explore their connections with similar notions for related types of imperfect symmetries (prefix inverse semigroup expansions,…
Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical…
We introduce a notion of $\varepsilon$-chains for continuous-time semiflows inspired by the shadow-orbit property. Although this definition differs from the $(\varepsilon,T)$-chains introduced by Conley, we prove that, for semiflows with…
In this paper the notion of global attractor is extended from the setting of semigroup actions on metric spaces to the setting of semigroup actions on uniformizable spaces. General conditions for the existence of global attractor are…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…
In a recent article, we introduced the concept of streams and graphs of a semiflow. An important related concept is the one of semiflow with {\em compact dynamics}, which we defined as a semiflow $F$ with a {\em compact global trapping…
The chain relation, due to Conley, and the strong chain relation, due to Easton, are well studied for continuous maps on compact metric spaces. Following Fathi and Pageault, we use barrier functions to generalize the theory to general…
We introduce and analyze the following general concept of recurrence. Let $G$ be a group and let $X$ be a G-space with the action $G\times X\longrightarrow X$, $(g,x)\longmapsto gx$. For a family $\mathfrak{F}$ of subset of $X$ and $A\in…
Considering any dense subsemigroup of the additive semigroup of positive real numbers and a filter associated with it as the domain of thought, various concepts of sets like sets that forces recurrence near zero, sets that contains broken…
We study qualitative properties of the set of recurrent points of finitely generated free semigroups of measurable maps. In the case of a single generator the classical Poincare recurrence theorem shows that these properties are closely…
We develop the attractors theory for the semigroups with multidimensional time belonging to some closed cone in an Euclidean space and apply the obtained general results to partial differential equations (PDEs) in unbounded domains. The…