[EN] We provide a sufficient condition for an operator T on a non-metrizable and sequentially
separable topological vector space X to be sequentially hypercyclic. This condition is
applied to some particular examples, ...
In this paper, we will study the chaotic behaviour, in the sense of Devaney, of infinite-dimensional linear systems on Banach spaces, especially we will study the solution C 0-semigroups of operators of these systems. 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 ...
Conejero Casares, José Alberto; Martínez Jiménez, Félix(Springer Verlag (Germany), 2011-09)
We give sufficient conditions for chaos of (differential) operators on Hilbert spaces of entire functions. To this aim we establish conditions on the coefficients of a polynomial P(z) such that P(B) is chaotic on the space ...
Beltrán Meneu, María José; Bonet Solves, José Antonio; Fernández, Carmen(American Institute of Mathematical Sciences (AIMS), 2015-02)
We study the integration operator, the differentiation operator
and more general differential operators on radial Fr´echet or (LB) H¨ormander
algebras of entire functions. We analyze when these operators are power
bounded, ...
Bes, J.; Martin O.; Peris Manguillot, Alfredo(Elsevier, 2011)
We characterize disjoint hypercyclicity and disjoint supercyclicity of finitely many linear fractional composition operators acting on spaces of holomorphic functions on the unit disc, answering a question of Bernal-González. ...
Bès, Juan P.; Martin, Özgür; Peris Manguillot, Alfredo; Shkarin, Stanislav A.(Elsevier, 2012-09-01)
Chan and Shapiro showed that each (non-trivial) translation operator f(z){mapping} Tλf(z+λ) acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal ...
In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, ...
Albanese, Angela A.; Barrachina Civera, Xavier; Mangino, Elisabetta Maria; Peris Manguillot, Alfredo(American Institute of Mathematical Sciences (AIMS), 2013-09)
Distributional chaos for strongly continuous semigroups is studied and characterized. It is shown to be equivalent to the existence of a distributionally irregular vector. Finally, a sufficient condition for distributional ...
Bonet Solves, José Antonio; Domański, Paweł(Cambridge University Press, 2012-11)
We study the dynamical behaviour of composition operators C φ defined on spaces A(Ω) of real analytic functions on an open subset Ω of ℝ d. We characterize when such operators are topologically transitive, i.e. when for ...
Bernardes, N. C., Jr.; Bonilla, A.; Peris Manguillot, Alfredo(Elsevier, 2020-02-01)
[EN] We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics ...
We study mixing properties (topological mixing and weak mixing of arbitrary order) for nonautonomous linear dynamical systems that are induced by the corresponding dynamics on certain invariant sets. The kinds of nonautonomous ...
We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) ...
[EN] We study a version of the specification property for linear dynamics. Operators having the specification property are investigated, and relationships with other well known dynamical notions such as mixing, Devaney ...
[EN] We generalize the notions of hypercyclic operators, U-frequently hypercyclic operators and frequently hypercyclic operators by introducing a new concept in linear dynamics, namely A-hypercyclicity. We then state an ...
Jiménez-Munguía, R. R; Martínez-Avendaño, Rubén A.; Peris Manguillot, Alfredo(Elsevier, 2013-06-02)
A bounded linear operator T on a Banach space X is called subspace-hypercyclic for a subspace M if Orb. (T, x) ∩ M is dense in M for a vector x∈ M. We show examples that answer some questions posed by H. Rezaei (2013) [7]. ...
We construct strongly mixing invariant measures with full support for operators on F-spaces which satisfy the Frequent Hypercyclicity Criterion. For unilateral backward shifts on sequence spaces, a slight modification shows ...
[EN] Given a Furstenberg family F of subsets of N, an operator T on a topological vector space X is called F-transitive provided for each non-empty open subsets U, V of X the set {n is an element of Z(+) : T-n (U) boolean ...
We characterize when backward shift operators defined on Banach sequence spaces exhibit the strong specification property. In particular, within this framework, the specification property is equivalent to the notion of ...
Bartoll Arnau, Salud(Universitat Politècnica de València, 2016-03-10)
[EN] The dynamics of linear operators, namely linear dynamics, is mainly concerned with the behaviour of iterates of linear transformations. Hypercyclicity is the study of linear operators that possess a dense orbit. ...