相关论文: Skew Product Attractors and concavity
Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
We develop a "weak Wa\.zewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a…
This paper belongs to a series of papers devoted to the study of the structure of the non-wandering set of an A-diffeomorphism. We study such set $NW(f)$ for an $\Omega$-stable diffeomorphism $f$, given on a closed connected 3-manifold…
We establish a linearization criterion for skew products of contractions in any dimension. We prove their smooth or holomorphic parameter dependence. In the smooth setting, we use the language of tame Fr\'echet spaces. We apply our result…
This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are…
In [FJJK] the Sharkovski\u{i} Theorem was extended to periodic orbits of strips of quasiperiodic skew products in the cylinder. In this paper we deal with the following natural question that arises in this setting: Does Sharkovski\u{i}…
We show that there exist real quadratic maps of the interval whose attractors are computationally intractable. This is the first known class of such natural examples.
We study the dynamics of a superattracting skew product $f$ on the attracting basin. As the first strategy, we find out forward $f$-invariant wedge-shaped regions in the basin, on some of which $f$ is conjugate to monomial maps, and…
An important problem in analysis on fractals is the existence of a self-similar energy on finitely ramified fractals. The self-similar energies are constructed in terms of eigenforms, that is, eigenvectors of a special nonlinear operator.…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
The goal of this paper is to explain when basechange theorems for sheaves of spaces imply basechange for sheaves with coefficients in other presentable $\infty$-categories. We accomplish this by analyzing when the tensor product of…
This article is concerned with the convexity properties of universal covers of projective varieties. We study the relation between the convexity properties of the universal cover of X and the properties of the pullback map sending vector…
This article studies the problem whether two convex (concave) regression functions modelling the relation between a response and covariate in two samples differ by a shift in the horizontal and/or vertical axis. We consider a nonparametric…
This paper deals with the attractors of generic dynamical systems. We introduce the notion of epsilon-invisible set, which is an open set in which almost all orbits spend on average a fraction of time no greater than epsilon. For…
The dynamics of the web map with weak linear dissipation is studied. The evolution of the coexisting attractors and the structure of their basins while changing the dissipation and nonlinearity are revealed. It is shown that the structure…
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…
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…
Our basic concept is the set $\mathcal{E}(H)$ of effects on a finite dimensional complex Hilbert space $H$. If $a,b\in\mathcal{E}(H)$, we define the sequential product $a[\mathcal{I}]b$ of $a$ then $b$. The sequential product depends on the…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…