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Listar por palabra clave "Hypercyclic operators"

Mostrando ítems 1-20 de 25

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A hypercyclicity criterion for non-metrizable topological vector spaces

Peris Manguillot, Alfredo (Adam Mickiewicz University, 2018)

[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, ...
Chaos for the Dynamics of Toeplitz Operators

Bartoll Arnau, Salud; Jiménez-Munguía, Ronald Richard; Martínez-Avendaño, Rubén Alejandro; Peris Manguillot, Alfredo (MDPI AG, 2022-02)

[EN] Chaotic properties in the dynamics of Toeplitz operators on the Hardy-Hilbert space H-2(D) are studied. Based on previous results of Shkarin and Baranov and Lishanskii, a characterization of different versions of chaos ...
Chaos on Fuzzy Dynamical Systems

Martínez Jiménez, Félix; Peris Manguillot, Alfredo; Ródenas Escribá, Francisco De Asís (MDPI AG, 2021-11)

[EN] Given a continuous map f : X -> X on a metric space, it induces the maps f over bar :K(X) -> K(X), on the hyperspace of nonempty compact subspaces of X, and (f) over cap :F(X) -> F(X), on the space of normal fuzzy ...
Chaotic behaviour of birth-and-death models with proliferation

Aroza, Javier; Peris Manguillot, Alfredo (Taylor & Francis, 2012)

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 ...
Chaotic Behaviour on Invariant Sets of Linear Operators

Murillo Arcila, Marina; Peris Manguillot, Alfredo (Springer Verlag (Germany), 2015)

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 ...
Chaotic differential operators

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 ...
Classical operators on the Hörmander algebras

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, ...
Disjoint hypercyclic linear fractional composition operators

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. ...
Disjoint mixing operators

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 ...
Distributional chaos for operators with full scrambled sets

Martínez Jiménez, Félix; Oprocha, Piotr; Peris Manguillot, Alfredo (Springer Verlag (Germany), 2013-06)

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, ...
Distributional chaos for strongly continuous semigroups of operators

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 ...
Frequently recurrent operators

Bonilla, Antonio; Grosse-Erdmann, Karl G.; López-Martínez, Antoni; Peris Manguillot, Alfredo (Elsevier, 2022-12-15)

[EN] Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We ...
Hypercyclic composition operators on spaces of real analytic functions

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 ...
Mean Li-Yorke chaos in Banach spaces

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 ...
Mixing properties for nonautonomous linear dynamics and invariant sets

Murillo Arcila, Marina; Peris Manguillot, Alfredo (Elsevier, 2013-02)

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 ...
On the existence of polynomials with chaotic behaviour

Bernardes, Nilson C.; Peris Manguillot, Alfredo (Hindawi Publishing Corporation, 2013)

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) ...
Operators with the specification property

Bartoll Arnau, Salud; Martínez Jiménez, Félix; Peris Manguillot, Alfredo (Elsevier, 2016)

[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 ...
Recurrence properties of hypercyclic operators

Bès, Juan Pablo; Menet, Quentin; Peris Manguillot, Alfredo; Puig-De Dios, Yunied (Springer-Verlag, 2016)

[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 ...
Sets of periods for chaotic linear operators

Conejero, J. Alberto; Martínez Jiménez, Félix; Peris Manguillot, Alfredo; Ródenas Escribá, Francisco De Asís (Springer-Verlag, 2021-02-09)

[EN] We provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.
Some questions about subspace-hypercyclic operators

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]. ...