3,190,431 research outputs found
Fatou-Seydi Singhiam Sarr talks about her relationship with Detroit
No full textFatou-Seydi Singhiam Sarr speaks about her relationship with Detroit for Marcus Lyon's i.Detroit project. She discusses the components of culture, and how being a part of a community means being open and trusting with one another
The Fatou completion of a Fréchet function space and applications
Get PDFGiven a metrizable locally convex-solid Riesz space of measurable functions we provide a procedure to construct a minimal Fréchet (function) lattice containing it, called its Fatou completion. As an application, we obtain that the Fatou completion of the space of integrable functions with respect to a Fréchet-space-valued measure is the space of scalarly -integrable functions. Further consequences are also given.
doi:10.1017/S144678870900023
Fatou maps in dynamics
No full textWe study the dynamics of a holomorphic self-map f of complexprojective space of degree d>1 by utilizing the notion of aFatou map, introduced originally by Ueda (1997) and independentlyby the author (2000). A Fatou map is intuitively like an analyticsubvariety on which the dynamics of f are a normal family (such as a local stable manifold of a hyperbolic periodic point). We show that global stable manifolds of hyperbolic fixed points are given by Fatou maps. We further show that they are necessarily Kobayashi hyperbolic and are always ramified by f (and therefore any hyperbolic periodic point attracts a point of thecritical set of f). We also show that Fatou components arehyperbolically embedded in ℙn and that a Fatou component which is attracted to a taut subset of itself isnecessarily taut.Peer Reviewe
A Cr unimodal map with an arbitrary fast growth of the number of periodic points
Get PDFIn this paper we present a surprising example of a C(r) unimodal map of an interval f : I -> I whose number of periodic points P(n)(f) = vertical bar{x is an element of I : f(n) x = x}vertical bar grows faster than any ahead given sequence along a subsequence (n)k = 3(k). This example also shows that 'non-flatness' of critical points is necessary for the Martens de Melo van Strien theorem [M. Martens, W. de Melo and S. van Strien. Julia-Fatou-Sullivan theory for real one-dimensional dynamics. Acta Math. 168(3-4) (1992), 273-318] to hold
Escaping Fatou components with disjoint hyperbolic limit sets
Get PDFWe construct automorphisms of C2 of constant Jacobian with a cycle of escaping Fatou components, on which there are exactly two limit functions, both of rank 1. On each such Fatou component, the limit sets for these limit functions are two disjoint hyperbolic subsets of the line at infinity. In the literature there are currently very few examples of automorphisms of C2 with rank one limit sets on the boundary of Fatou components. To our knowledge, this is the first example in which such limit sets are hyperbolic, and moreover different limit sets of rank 1 coexist
Fatou and Korányi-Vági type theorems on the minimal ball
Get PDFIn this paper we develop the Hp (p [greater than or equal] 1) theory on the minimal ball. After identifying the admissible approach regions, we establish theorems of Fatou and Korányi-Vági type on this ball
On s-additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model
Get PDFRecently, Frittelli and Scandolo ([9]) extend the notion of risk measures, originally introduced by Artzner, Delbaen, Eber and Heath ([1]), to the risk assessment of abstract financial positions, including pay offs spread over different dates, where liquid derivatives are admitted to serve as financial instruments. The paper deals with s-additive robust representations of convex risk measures in the extended sense, dropping the assumption of an existing market model, and allowing also unbounded financial positions. The results may be applied for the case that a market model is available, and they encompass as well as improve criteria obtained for robust representations of the original convex risk measures for bounded positions ([4], [7], [16]).Convex risk measures, model uncertainty, s-additive robust representation, Fatou property, nonsequential Fatou property, strong s-additive robust representation, Krein-Smulian theorem, Greco theorem, inner Daniell stone theorem, general Dini theorem, Simons’ lemma.
Fatou and brothers Riesz theorems in the infinite-dimensional polydisc
Get PDFWe study the boundary behavior of functions in the Hardy spaces on the infinite-dimensional polydisc. These spaces are intimately related to the Hardy spaces of Dirichlet series. We exhibit several Fatou and Marcinkiewicz- Zygmund type theorems for radial convergence of functions with Fourier spectrum supported on N0∞∪(−N0∞). As a consequence one obtains easy new proofs of the brothers F. and M. Riesz Theorems in infinite dimensions, as well as being able to extend a result of Rudin concerning which functions are equal to the modulus of an H 1 function almost everywhere to T ∞ . Finally, we provide counterexamples showing that the pointwise Fatou theorem is not true in infinite dimensions without restrictions to the mode of radial convergence even for bounded analytic functions
Hyperbolic entire functions with bounded Fatou components
Get PDFAgraïments: The third author was supported by a Philip Leverhulme Prize.We show that an invariant Fatou component of a hyperbolic transcendental entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our results are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values
Fatou���Bieberbach Domains: A New Construction and a Theme on the Runge Property
Get PDFFatou���Bieberbach domains are a phenomenon specific to several complex variables. Techniques for producing such domains are limited and fundamental questions about containment between two Fatou���Bieberbach are still being raised. We show that given a countable collection of Runge Fatou���Bieberbach domains with a ball in common and a common point omitted, there exists a Runge Fatou���Bieberbach domain that contains the union.
Additionally, we provide a new construction for Fatou���Bieberbach domains modelled on the attracting basin, using right-side composition instead of the prototypical left-side composition. We use this construction to show that there exists a strictly decreasing family of Fatou���Bieberbach domains whose intersection contains a Fatou���Bieberbach domain. Additionally, we provide a generalized condition for constructing attracting basins from a sequence of automorphisms
- …
