Positive Transfer Operators and Decay of Correlations


Author: Viviane Baladi
Publisher: World Scientific
ISBN: 9814496669
Category: Science
Page: 324
View: 9122

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Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system “mixes”, i.e. “forgets” its initial conditions. This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained. The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum. Contents:Subshifts of Finite Type: A Key Symbolic ModelSmooth Uniformly Expanding DynamicsPiecewise Expanding SystemsHyperbolic Systems Readership: Physicists, mathematicians, interdisciplinary scientists and social scientists. Keywords:Transfer Operator;Spectrum;Thermodynamic Formalism;Correlation Function;Mixing;Dynamical System;Chaos;Equilibrium State;Spectral Gap;Perron Frobenius OperatorReviews: “The book can be used both as a textbook for beginners and as a reference book for workers in the field … the proofs are given in full, allowing a detailed study of the techniques and making the book nicely self-contained.” Mathematical Reviews

Modeling, Dynamics, Optimization and Bioeconomics I

Contributions from ICMOD 2010 and the 5th Bioeconomy Conference 2012
Author: Alberto Adrego Pinto,David Zilberman
Publisher: Springer
ISBN: 331904849X
Category: Mathematics
Page: 753
View: 4373

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This volume explores the emerging and current, cutting-edge theories and methods of modeling, optimization, dynamics and bio economy. It provides an overview of the main issues, results and open questions in these fields as well as covers applications to biology, economy, energy, industry, physics, psychology and finance. The majority of the contributed papers for this volume come from the participants of the International Conference on Modeling, Optimization and Dynamics (ICMOD 2010), a satellite conference of EURO XXIV Lisbon 2010, which took place at Faculty of Sciences of University of Porto, Portugal and from the Berkeley Bio economy Conference 2012, at the University of California, Berkeley, USA.

Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics


Author: Juan Carlos Pardo Millán,Pedro Solórzano
Publisher: American Mathematical Soc.
ISBN: 1470442868
Category: Mathematicians
Page: N.A
View: 7492

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This volume contains the proceedings of the Second Workshop of Mexican Mathematicians Abroad (II Reunión de Matemáticos Mexicanos en el Mundo), held from December 15–19, 2014, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. This meeting was the second in a series of ongoing biannual meetings aimed at showcasing the research of Mexican mathematicians based outside of Mexico. The book features articles drawn from eight broad research areas: algebra, analysis, applied mathematics, combinatorics, dynamical systems, geometry, probability theory, and topology. Their topics range from novel applications of non-commutative probability to graph theory, to interactions between dynamical systems and geophysical flows. Several articles survey the fields and problems on which the authors work, highlighting research lines currently underrepresented in Mexico. The research-oriented articles provide either alternative approaches to well-known problems or new advances in active research fields. The wide selection of topics makes the book accessible to advanced graduate students and researchers in mathematics from different fields.

European Congress of Mathematics, Barcelona, July 10-14, 2000

Vol. 1
Author: Spain) European Congress of Mathematics 2000 (Barcelona
Publisher: Springer Science & Business Media
ISBN: 9783764364175
Category: Mathematics
Page: 582
View: 757

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The Third European Congress of Mathematics (3ecm) took place from July 10th to July 14th, 2000 in Barcelona. It was organised by the Societat Catalana de Matematiques (Catalan Mathematical Society), under the auspices of the Euro­ pean Mathematical Society (EMS). As foreseen by the EMS and the International Mathematical Union, this Congress was a major event in World Mathematical Year 2000. In addition to reviewing outstanding research achievements, important aspects of the life of European mathematics were discussed. Mathematics is undergoing a period of rapid changes. Effective computation and applications in science and technology go ever more hand in hand with con­ ceptual developments. It was one of the aims of 3ecm to reflect this mutual enrich­ ment, while steering present and future trends of mathematical sciences. In fact, the motto of the Congress, Shaping the 21st Century, was meant to capture these views. Nearly 1400 people from 87 countries gathered together in the Palau de Con­ gressos of Barcelona in order to take part in the activities of the 3ecm scientific programme: Nine plenary lectures, thirty invited lectures in parallel sessions, lec­ tures given by EMS prize winners, ten mini-symposia on special topics, seven round tables, poster sessions, presentations of mathematical software and video exhibitions. Twenty events were satellites of 3ecm in various countries.

Harmonic Analysis and Rational Approximation

Their Rôles in Signals, Control and Dynamical Systems
Author: Jean-Daniel Fournier
Publisher: Springer Verlag
ISBN: 9783540309222
Category: Science
Page: 311
View: 3296

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Research in Interactive Design presents an in-depth study of new product design methods. Interactive design is an original structured design approach that has recently emerged from transversal research. On the research side, the topic of interactive design is the fruitful result of sophisticated joint studies combining specific numerical engineering theories, original development in design science and industrial engineering, new discoveries in mechatronics and advanced mechanical engineering methods. Additionally, industry benefits from interactive design instruments. Interactive design is a constructive approach that tends to ensure innovation by improving user-integration in the design process, fostering the development of virtual prototypes and providing new powerful ways for collaborative design activities. Interactive design instruments are seen as the extension of traditional CAD tools. This book provides an accurate overview of the recent research or industrial application in interactive design. The different arguments, taken from the international conference Virtual Concept 2005, will provide the reader with some advanced solutions concerning new methods and tools by discussing: - modelling techniques: new techniques ensuring the development of high qualified, updated and reduced models being able to represent the behaviour of a process or a product in its environment; - design solution space exploration: specific instruments dedicated to the identification of suitable design solutions and their virtual representation allowing engineers to have interaction with the virtual worlds; - interactive process organization: studies highlighting the basic evolutions of a process integrating new instruments of interactive design. Each subsequent part of the book addresses both advanced techniques and industrial applications of the latest successful research in interactive design. The solutions presented are enhanced by demonstration

Journal of Physics

Mathematical and general
Author: Institute of Physics (Great Britain)
Publisher: N.A
ISBN: N.A
Category: Mathematical physics
Page: N.A
View: 2369

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Semiclassical Analysis, Witten Laplacians, and Statistical Mechanics


Author: Bernard Helffer
Publisher: World Scientific
ISBN: 9789812380982
Category: Mathematics
Page: 179
View: 5997

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This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality.

Die Lehre von den Kettenbrüchen

Band I: Elementare Kettenbrüche
Author: Oskar Perron
Publisher: Springer-Verlag
ISBN: 3663122891
Category: Mathematics
Page: 194
View: 7300

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eigenen Begriffssystemen bereichert worden, die man nicht gerade als jedermann geläufig voraussetzen darf. Die Versuchung lag nahe, durch Heranziehung solcher Theorien den Kettenbrüchen einen gelehrteren Anstrich zu geben. Aber dadurch wäre nicht nur die Lektüre unnötig erschwert, sondern das Wesen der Dinge zumeist verschleiert worden, und es bestände die Gefahr, daß mancher Leser den künstlichen Anstrich für das Wesentliche halten und die harmlose Unschuld, die sich darunter verbirgt, vielleicht gar nicht mehr sehen würde. Deshalb habe ich auf logistische Hieroglyphen, geheimnisvolle "Räume" usw. verzichtet und bin bei der klassischen Wortsprache und den klassischen Rechenmethoden ge blieben. Lediglich zweireihige Matrizes wurden gelegentlich verwandt, nämlich da, wo sie einen wirklichen methodischen Vorteil bieten. Der Matrixkalkül ist ja heute in viel weiteren Kreisen bekannt als vor 40 Jahren und gehört fast schon zu den Elementen; ich habe ihn trotzdem nicht vorausgesetzt, sondern in § 5 das Wenige, was davon gebraucht wird, kurz zusammengestellt. In neuerer Zeit haben die Kettenbrüche auch in der augewandten Mathematik, z. B. in der Elektrotechnik und bei analytischen Approximationsmethoden, Verwendung ge funden. Auch den Vertretern dieser Disziplinen, sowie manchen interessierten Laien, die es trotz unseres materialistischen Zeitalters doch immer noch gibt, glaube ich durch leichte Verständlichkeit besser zu dienen als durch Paradieren mit einer übertriebenen Gelehrsamkeit. Auf die Beigabe einer möglichst lückenlosen Bibliographie habe ich ebenso wie früher verzichtet; man findet eine solche, die von den Anfängen bis ins erste Jahrzehnt unseres Jahrhunderts reicht, bei Wölffing 1.

Vorlesungen über Atommechanik


Author: M. Born
Publisher: Springer-Verlag
ISBN: 3642618987
Category: Science
Page: 358
View: 3595

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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.