Results 51 to 60 of about 108 (97)
Frequently Hypercyclic Random Vectors
, 2023 Some results concerning the existence of almost surely frequently hypercyclic random vectors have been proved in the literature for certain chaotic weighted shifts. This is of interest for at least two reasons. It is usually difficult to find explicit (frequently) hypercyclic vectors, and random vectors have a probability distribution whose ergodic ...
openaire +1 more source
Common hypercyclic vectors for families of backward shift operators [PDF]
Journal of Operator Theory, 2017 We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the full orbit of the backward shift.
openaire +2 more sources
Common hypercyclic vectors for certain families of differential operators [PDF]
Illinois Journal of Mathematics, 2016 Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers . We consider a specific sequence of differential operators Tk(n),λ , n=1,2,... on the space of entire functions , that depend on the sequence (k(n)) n=1,2,... and the non-zero complex number λ .
openaire +3 more sources
Discrete cyclic systems and circle congruences. [PDF]
Ann Mat Pura Appl, 2022 Hertrich-Jeromin U, Szewieczek G.
europepmc +1 more source
Invariant manifolds of hypercyclic vectors for the real scalar case [PDF]
Proceedings of the American Mathematical Society, 1999 We show that every hypercyclic operator on a real locally convex vector space admits a dense invariant linear manifold of hypercyclic vectors.
openaire +3 more sources
An operator on a separable Hilbert space with many hypercyclic vectors [PDF]
Studia Mathematica, 1987 Let T be a linear continuous operator acting in a Hilbert space H. A point \(x_ 0\in H\) is said to be cyclic if \(H=span(x_ 0,Tx_ 0,T\) \(2x_ 0,...)\) and hypercyclic if the orbit \((x_ 0,Tx_ 0,T\) \(2x_ 0,...)\) is dense in H. There is given a construction of a separable Hilbert space H (over complexes) and an operator T with a cyclic vector \(x_ 0\)
openaire +1 more source
Common frequently hypercyclic random vectors
We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a non-existence result.
Mouze, Augustin, Munnier, Vincent
openaire +2 more sources
Frequently hypercyclic random vectors for $C_{0}$ -semigroups
Ergodic Theory and Dynamical SystemsAbstract We show that, under certain conditions, a strongly continuous semigroup admits an almost surely frequently hypercyclic random vector defined as a stochastic integral in Fréchet spaces with respect to the Brownian motion. Two criteria are given.
openaire +2 more sources
Luh hypercyclic vector for composition operator
In this paper, we deal with the construction of holomorphic functions on a simply connected domain satisfying that all its derivatives and antiderivatives under a composition operator have a dense orbit. Such functions will be called Luh hypercyclic vectors for the respective composition operator.
Benchiheb, Otmane +3 more
openaire +2 more sources