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- FRÉDÉRIC BAYART, SOPHIE GRIVAUX
- 2006

We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators T on separable complex F-spaces: T is frequently hypercyclic if there exists a vector x such that for every nonempty open subset U of X, the set of integers n such that T n x belongs to U has positive lower density. We give several criteria… (More)

- Frédéric BAYART, Lucas QUARTA, Frédéric Bayart, Lucas Quarta
- 2006

We show that the set of continuous nowhere differen-tiable functions, the set of Dirichlet series which are bounded in the right half-plane and diverge everywhere on the imaginary axis, and the set of continuous interpolating functions contain big algebras.

This study extends an examination of the behavioral and pituitary-adrenal responses of infant squirrel monkeys (Saimiri sciureus) separated from their mothers under different environmental conditions to another physiological system by measuring the metabolites of the central monoamines found in the cerebrospinal fluid (CSF). This study included… (More)

The effects of maternal proximity on the behavioral and physiological responses of infant rhesus macaques during 4 days of total or adjacent separations from the mother were studied. The 6 infants tested showed behavioral responses that differentiated the two separation conditions. Major differences were found in the quantity and quality of vocalizations,… (More)

This study examined reactions to mirror-image stimulation in a wild- reared adult male monkey (Macaca tonkeana) which had spontaneously developed a form of tool-use, namely the use of plant stems to reach mucus inside the nose. Initial intense social responsiveness to the mirror was followed by habituation, although some social responding persisted. Mirror-… (More)

- FRÉDÉRIC BAYART
- 2013

We prove that, in the Baire category sense, a typical measure supported by a compact set admits a linear lower singularity spectrum. We investigate the same question for the upper singularity spectrum and for other forms of genericity.

We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series , which we call the Wiener-Dirichlet algebra, namely the connection between the properties of the operator and of its symbol, with special emphasis on the compact, automorphic, or isometric character of this… (More)

- FRÉDÉRIC BAYART, YANICK HEURTEAUX
- 2011

We study the size, in terms of the Hausdorff dimension, of the subsets of T such that the Fourier series of a generic function in L 1 (T), L p (T) or in C(T) may behave badly. Genericity is related to the Baire category theorem or to the notion of prevalence. This paper is a continuation of [2].

We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on ℓ p (Z), p ≥ 1. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is U-frequently hypercyclic, yet not frequently hypercyclic and that… (More)

- FRÉDÉRIC BAYART
- 2008

We study the existence of a common hypercyclic vector for different families of composition operators. We also give a continuous version of Salas theorem on weighted shifts. A continuous operator acting on a topological vector space X is called hy-percyclic provided there exists a vector x ∈ X such that its orbit {T n x; n ≥ 1} is dense in X. Such a vector… (More)