Related papers: Dynamics of Induced Systems

This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an…

Let $\mathcal{M}(X)$ be the space of Borel probability measures on a compact metric space $X$ endowed with the weak$^\ast$-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system…

We consider the dynamics of a meromorphic map on a compact kahler surface whose topological degree is smaller than its first dynamical degree. The latter quantity is the exponential rate at which its iterates expand the cohomology class of…

Discrete dynamical systems defined by the iteration of a polynomial map of the unit simplex to itself appear in the context of population genetic systems evolving under mutation, recombination and weak selection. Although exceptional…

We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply…

This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory…

In this paper, we investigate various cardinal properties of the space $Q_{C}X$ of all real-valued quasicontinuous functions on the topological space $X$, under the topology of uniform convergence on compact subsets. It begins by examining…

We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…

Let $M$ be a compact Riemannian manifold. The set $\text{F}^{r}(M)$ consisting of sequences $(f_{i})_{i\in\mathbb{Z}}$ of $C^{r}$-diffeomorphisms on $M$ can be endowed with the compact topology or with the strong topology. A notion of…

We analyse the structure of the quotient $\mathrm{A}_\sim(\Gamma,X,\mu)$ of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This space carries a natural operation of convex…

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…

We study a series of dynamical concepts for self-maps in the primal topology induced by them. Among the concepts studied are non-wandering points, limit points, recurrent points, minimal sets, transitive points and self-maps, topologically…

One point compactification is studied in the light of ideal of subsets of $\mathbb{N}$. $\mathcal{I}$-proper map is introduced and showed that a continuous map can be extended continuously to the one point $\mathcal{I}$-compactification if…

For a topological dynamical system we characterize the decomposition of the state space induced by the fixed space of the corresponding Koopman operator. For this purpose, we introduce a hierarchy of generalized orbits and obtain the finest…

A topological constraint on the dynamics of a magnetic field in a flux tube arises from the fixed point indices of its field line mapping. This can explain unexpected behaviour in recent resistive-magnetohydrodynamic simulations of magnetic…

Here we analyze the behavior of dynamically coupled maps, based on those introduced in a series of papers by Ito and Kaneko (Phys. Rev. Lett. 88:028701, 2002 and Phys. Rev. E 67:046226, 2003). We show how the microscopic coupling mechanism…

In order to determine the dynamics of nonautonomous equations both their forward and pullback behavior need to be understood. For this reason we provide sufficient criteria for the existence of such attracting invariant sets in a general…

A translation structure on a surface is an atlas of charts to the plane so that the transition functions are translations. We allow our surfaces to be non-compact and infinite genus. We endow the space of all pointed surfaces equipped with…

In this work, we show that if $f$ is a uniformly continuous map defined over a Polish metric space, then the set of $f$-invariant measures with zero metric entropy is a $G_\delta$ set (in the weak topology). In particular, this set is…

We review some relations occurring between the combinatorial intersection theory on the moduli spaces of stable curves and the asymptotic behavior of the 't Hooft-Kontsevich matrix integrals. In particular, we give an alternative proof of…