1,720,984 research outputs found
Quasianalytic monogenic solutions of a cohomological equation
Full text linkWe prove that the solutions of a cohomological equation of complex dimension one and in the
analytic category have a monogenic dependence on the parameter, and we investigate the question
of their quasianalyticity. This cohomological equation is the standard linearized conjugacy equation
for germs of holomorphic maps in a neighborhood of a fixed point. The parameter is the eigenvalue
of the linear part, denoted by q.
Borel’s theory of non-analytic monogenic functions has been first investigated by Arnol’d and
Herman in the related context of the problem of linearization of analytic diffeomorphisms of the
circle close to a rotation. Herman raised the question whether the solutions of the cohomological
equation had a quasianalytic dependence on the parameter q. Indeed they are analytic for q ∈ CS
1
,
the unit circle S
1 appears as a natural boundary (because of resonances, i.e. roots of unity), but
the solutions are still defined at points of S
1 which lie “far enough from resonances”. We adapt to
our case Herman’s construction of an increasing sequence of compacts which avoid resonances and
prove that the solutions of our equation belong to the associated space of monogenic functions ;
some general properties of these monogenic functions and particular properties of the solutions are
then studied.
For instance the solutions are defined and admit asymptotic expansions at the points of S
1
which satisfy some arithmetical condition, and the classical Carleman Theorem allows us to answer
negatively to the question of quasianalyticity at these points. But resonances (roots of unity) also
lead to asymptotic expansions, for which quasianalyticity is obtained as a particular case of Ecalle’s ́
theory of resurgent functions. And at constant-type points, where no quasianalytic Carleman class
contains the solutions, one can still recover the solutions from their asymptotic expansions and
obtain a special kind of quasianalyticity.
Our results are obtained by reducing the problem, by means of Hadamard’s product, to the
study of a fundamental solution (which turns out to be the so-called q-logarithm or “quantum
logarithm”). We deduce as a corollary of our work the proof of a conjecture of Gammel on the
monogenic and quasianalytic properties of a certain number-theoretical Borel-Wolff-Denjoy series
Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps.
No full textFor a piecewise expanding unimodal interval map f with unique absolutely continuous invariant probability measure μ, a perturbation X, and an observable φ, the susceptibility function is Ψφ(z)=∑∞k=0zk∫X(x)φ′(fk)(x)(fk)′(x)dμ. Combining previous results [V. Baladi, On the susceptibility function of piecewise expanding interval maps. Comm. Math. Phys. 275 (2007), 839–859; V. Baladi and D. Smania, Linear response for piecewise expanding unimodal maps. Nonlinearity 21 (2008), 677–711] (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer–Simon [Natural boundaries and spectral theory. Adv. Math. 226 (2011), 4902–4920] (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon [Sur les séries de Dirichlet. Ann. Sci. Éc. Norm. Supér. (3) 66 (1949), 263–310]), we show that density of the postcritical orbit (a generic condition) implies that Ψφ(z) has a strong natural boundary on the unit circle. The Breuer–Simon method provides uncountably many candidates for the outer functions of Ψφ(z), associated with precritical orbits. If the perturbation X is horizontal, a generic condition (Birkhoff typicality of the postcritical orbit) implies that the non-tangential limit of Ψφ(z) as z→1 exists and coincides with the derivative of the absolutely continuous invariant probability measure with respect to the map (‘linear response formula’). Applying the Wiener–Wintner theorem, we study the singularity type of non-tangential limits of Ψφ(z) as z→eiω for real ω. An additional ‘law of the iterated logarithm’ typicality assumption on the postcritical orbit gives stronger results
On the regularity of Mather's β-function for standard-like twist maps
Full text linkWe consider the minimal average action (Mather's β function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the β-function associated to a standard-like twist map admits a unique C1-holomorphic (canonical) complex extension, which coincides with this function on the set of real diophantine frequencies. In particular, we deduce a uniqueness result for Mather's β function
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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