Results 41 to 50 of about 752 (101)
Common hypercyclic vectors and dimension of the parameter set
Indiana University Mathematics Journal, 2022 We investigate the existence of a common hypercyclic vector for a family $(T_ )_{ \in }$ of hypercyclicoperators acting on the same Banach space $X$. We give positive and negative results involving the dimension of $ $ and the regularity of each map $ \in \mapsto T_ ^n x$, $x\in X$, $n\in\mathbb N$.
Bayart, Frédéric +2 more
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, 2013 In this note we prove a Birkhoff type transitivity theorem for continuous maps acting on non-separable completely metrizable spaces and we give some applications for dynamics of bounded linear operators acting on complex Fr\'{e}chet spaces. Among them we
Manoussos, Antonios
core +1 more source
On Some Subspace Codiskcyclic Operators in Banach Spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.This paper introduces the concepts of subspace codiskcyclicity and subspace codisk transitivity, providing criteria and examples that highlight their distinct properties compared to traditional codiskcyclic operators and hypercyclic operators. The paper also demonstrates the existence of subspace codiskcyclic operators in finite‐dimensional Banach ...
Peter Masong Slaa +3 more
wiley +1 more source
Frequently Hypercyclic and Chaotic Behavior of Some First‐Order Partial Differential Equation
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We study a particular first‐order partial differential equation which arisen from a biologic model. We found that the solution semigroup of this partial differential equation is a frequently hypercyclic semigroup. Furthermore, we show that it satisfies the frequently hypercyclic criterion, and hence the solution semigroup is also a chaotic semigroup.
Cheng-Hung Hung +2 more
wiley +1 more source
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
wiley +1 more source
Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations
Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 The notion of distributional chaos has been recently added to the study of the linear dynamics of operators and C0‐semigroups of operators. We will study this notion of chaos for some examples of C0‐semigroups that are already known to be Devaney chaotic.
Xavier Barrachina +2 more
wiley +1 more source
Multiplicative structures of hypercyclic functions for convolution operators
, 2017 In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given entire ...
Bernal-González, Luis +3 more
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Abstract and Applied Analysis, Volume 2024, Issue 1, 2024.In this paper, under appropriate hypotheses, we have the existence of a solution semigroup of partial differential equations with delay operator. These equations are used to describe time–age‐structured cell cycle model. We also prove that the solution semigroup is a frequently hypercyclic semigroup.
Cheng-Hung Hung, Victor Kovtunenko
wiley +1 more source
Existence and nonexistence of hypercyclic semigroups [PDF]
, 2007 In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from –and considerably shorter than– the one recently given by ...
Bernal González, Luis +1 more
core
Linear Subspaces of Hypercyclic Vectors
Real Analysis Exchange, 2018 In my talk I presented results from previous papers on the existence of hypercyclic algebras for convolution operators acting on the space of entire functions.
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