1,720,981 research outputs found
Transfer operators for piecewise affine approximations of interval maps
No full textWe consider a natural approximation scheme for piecewise expanding, piecewise C1+Lipschitz, mixing Markov interval maps f by piecewise affine maps. We prove that the densities of the absolutely continuous invariant probability measures of the approximations converge exponentially fast to the density of the absolutely continuous invariant probability measure of f in the uniform norm. To do this we compare the relevant transfer operators of the approximations with that of f , and u s e
recently developed perturbation techniques
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
Exponential decay of correlations for finite horizon Sinai billiard flows
No full textWe prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L-t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions
Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables
No full textWe consider a smooth one-parameter family t → ( ft : M → M) of diffeomorphisms with compact transitive Axiom A attractors λt denoting by dpt the SRB measure of fttλt. Our first result is that for any function θ in the Sobolev space Hrp(M), with 1π-rfpagπ ∞ and 0 π r π 1/p, the map tx→ ∫ θ dpt is ?-Hölder continuous for all r. This applies to(x) = h(x) θ (g(x) ? a) (for all >1) for h and g smooth and θ the Heaviside function, if a is not a critical value of g. Our second result says that for any such function -(x) = h(x) θ (g(x) ? a) so that in addition the intersection of {x|g(x) = a} with the support of h is foliated by admissible stable leaves of ft, the map t d-t is differentiable. (We provide distributional linear response and fluctuation-dissipation formulas for the derivative.) Obtaining linear response or fractional response for such observables θ is motivated by extreme-value theory
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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