Results 51 to 60 of about 126 (118)
Analytic Automorphisms and Transitivity of Analytic Mappings
Mathematics, 2020 In this paper, we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators.
Zoriana Novosad, Andriy Zagorodnyuk
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Journal of Functional Analysis, 2003 A (bounded) operator \(T\) on a complex infinite-dimensional separable Banach space \(X\) is said to be hypercyclic if there is a (hypercyclic) vector \(x \in X\) such that its orbit \(O(T,x):=\{x,Tx,T^2x,\dots\}\) is dense in \(X\). The operator \(T\) is called chaotic if it is hypercyclic and the set of periodic points of \(T\) is dense in \(X ...
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Interactions between universal composition operators and complex dynamics
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract This paper is concerned with universality properties of composition operators Cf$C_f$, where the symbol f$f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of Cf$C_f$ when f$f$ is restricted to (subsets of) Baker and wandering domains.
Vasiliki Evdoridou +2 more
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The Strong Disjoint Blow‐Up/Collapse Property
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 Let X be a topological vector space, and let ℬ(X) be the algebra of continuous linear operators on X . The operators T1, …, TN ∈ ℬ(X) are disjoint hypercyclic if there is x ∈ X such that the orbit {(T1n(x),…,TNn(x)):n∈ℕ} is dense in X × …×X . Bès and Peris have shown that if T1, …, TN satisfy the Disjoint Blow‐up/Collapse property, then they are ...
Héctor N. Salas, Ajda Fošner
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Dynamics of differentiation operators on generalized weighted Bergman spaces
Open Mathematics, 2014 The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous.
Zhang Liang, Zhou Ze-Hua
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Hypercyclic Composition Operators
Journal of Vasyl Stefanyk Precarpathian National University, 2015 In this paper we give survey of hypercyclic composition operators. In pacticular,we represent new classes of hypercyclic composition operators on the spaces of analyticfunctions
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Spaces that admit hypercyclic operators with hypercyclic adjoints [PDF]
Proceedings of the American Mathematical Society, 2005 A continuous linear operator T : X →
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Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.This article extends Alfredo Peris’s work on chaos in set‐valued dynamics by providing new characterizations and applications of transitivity and mixing properties. Peris demonstrated that the topological transitivity of a set‐valued map is closely related to the weak mixing property of the individual map.
Illych Alvarez, Mehmet Ünver
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On the Weakly Hypercyclic Composition Operators on Hardy Spaces
Journal of Mathematical Extension, 2010 An operator T on a Banach space X is said to be weakly hypercyclic if there exists a vector x ∈ X whose orbit under T is weakly dense in X. We show that every weakly hypercyclic composition operator on classic Hardy space H2 is norm hypercyclic.
H. Rezaei
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On locally finite groups whose derived subgroup is locally nilpotent
Mathematische Nachrichten, Volume 297, Issue 12, Page 4389-4400, December 2024.Abstract A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This result has been extended to saturated formations in Ballester‐Bolinches, Ezquerro, and Pedreza‐Aguilera [Math. Nachr.
Marco Trombetti
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