Frequently dense orbits

By K. Grosse-Erdmann, Alfredo Peris. 2005

53 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f6766de22a3801f1281925576594b09cea0597a

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Hypercyclic behaviour of operators in a hypercyclic C 0 -semigroup (2007, background): “1 The first and third authors were supported in part by MEC and FEDER, Project MTM2004-02262 and Research Net MTM2006-26627-E 2 The second author was partially supported by grant No. 201/06/0128 of GA ČR”
Frequently hypercyclic operators and vectors (2007, background): “10 of [3], by which this necessary condition would also be sufficient in the case X = l, was recently disproved by Peris and the second author [15].”
Linear dynamical systems on Hilbert spaces: typical properties and explicit examples (2017, background): “Apart from this consequence of [33], nothing seems to be known concerning this question from [6].”
Recurrence properties of hypercyclic operators (2014, background): “Thanks to Grosse-Erdmann and Peris [17], we know that every frequently hypercyclic operator is weakly mixing.”
Szemeredi's theorem, frequent hypercyclicity and multiple recurrence (2010, background): “Is it true that for every positive integer N ≥ 2 the operator T ⊕ T 2 ⊕ · · · ⊕ T m is hypercyclic? Recall that Grosse-Erdmann and Peris have shown that in this case T ⊕ T is hypercyclic; see [28].”
Invariant Gaussian measures for operators on Banach spaces and linear dynamics (2007, background): “The work of Grosse-Erdmann and Peris in [16] emphasizes the importance of the behaviour of the product w1 .”
Difference sets and frequently hypercyclic weighted shifts (2013, background): “A necessary condition for Bw to be frequently hypercyclic was given in [2] and improved in [11].”
Unimodular eigenvalues, uniformly distributed sequences and linear dynamics (2007, methodology): “Grosse-Erdmann and Peris proved in [20] that every frequently hypercyclic operator satisfies the Hypercyclicity Criterion.”