Related papers: Generalized Hyperbolicity, Stability and Expansivi…

We examine the chaotic behavior of certain continuous linear operators on infinite-dimensional Banach spaces, and provide several equivalent characterizations of when these operators have infinite topological entropy. For example, it is…

We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.

We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. In contrast with the complex case, we observe…

In the present article, it is proved that every nuclear operator in a locally convex space E has a well-defined trace if E possesses the approximation property. However, even if a space possesses the approximation property this still does…

For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…

We prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This…

In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…

We study density properties of orbits for a hypercyclic operator $T$ on a separable Banach space $X$, and show that exactly one of the following four cases holds: (1) every vector in $X$ is asymptotic to zero with density one; (2) generic…

The standard theory of Banach spaces is built upon the notions of vector space, triangle inequality and Cauchy completeness. Here we propose a `hyperbolic' variant of this `elliptic' framework where general linear combinations are replaced…

We discuss the dynamics of $n$-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every $n\in\mathbb{N}$, we exhibit an $n$-expansive homeomorphism, which is not $(n-1)$-expansive, has the shadowing…

In this article, we first prove the existence of an invariant subspace for a norm-attaining $\ast$-paranormal operator. Then give a representation for $\ast$-paranormal operators in the closure of absolutely norm-attaining operators and…

Since the solution of the so-called folk problems of smoothability, there has been a special interest in the properties of classical time and volume functions of spacetimes. Here we supply some information that complements the one provided…

Let $\Om$ be a unbounded domain in a Banach space. In this work, we wish to impose {\it local conditions} on boundary point of $\Om$ (including the point at infinity) that guarantee complete hyperbolic of $\Om.$ We also search for local…

In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are…

We introduce continuum-wise hyperbolicity, a generalization of hyperbolicity with respect to the continuum theory. We discuss similarities and differences between topological hyperbolicity and continuum-wise hyperbolicity. A shadowing lemma…

The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

We study hypercyclicity, Devaney chaos, topological mixing properties and strong mixing in the measure-theoretic sense for operators on topological vector spaces with invariant sets. More precisely, our purpose is to establish links between…

In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we…