Positive Transfer Operators and Decay of Correlations


Author: Viviane Baladi
Publisher: World Scientific
ISBN: 9789810233280
Category: Science
Page: 314
View: 5038

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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.

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: 1770

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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: 2704

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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: Carles Casacuberta
Publisher: Springer Science & Business Media
ISBN: 9783764364175
Category: Mathematics
Page: 582
View: 8560

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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: 8482

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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

Chaotic Billiards


Author: Nikolai Chernov,Roberto Markarian
Publisher: American Mathematical Soc.
ISBN: 0821840967
Category: Mathematics
Page: 316
View: 604

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This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject.The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.

Geometrical Theory of Dynamical Systems and Fluid Flows

Revised
Author: Tsutomu Kambe
Publisher: World Scientific Publishing Company
ISBN: 981310760X
Category: Science
Page: 444
View: 4214

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This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics.

Linear Operators and their Spectra


Author: E. Brian Davies
Publisher: Cambridge University Press
ISBN: 1139464337
Category: Mathematics
Page: N.A
View: 2301

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This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.

Smooth Dynamical Systems


Author: M. C. Irwin
Publisher: World Scientific
ISBN: 9810245998
Category: Mathematics
Page: 259
View: 1799

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This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area.

Rayleigh-Bénard Convection

Structures and Dynamics
Author: A V Getling
Publisher: World Scientific
ISBN: 9814498971
Category: Science
Page: 256
View: 9544

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This invaluable book presents a concise but systematic account of the formation of spatial flow structures in a horizontal fluid layer heated from below. Flows of this type, known as Rayleigh-Bénard convection, show important features of behaviour inherent not only in various hydrodynamic-instability phenomena but also in nonlinear pattern-forming processes in other contexts. The book describes the basic methods of investigating convection patterns, and the types of two- and three-dimensional flows, pattern defects, and sequences of convection-regime changes. The author pays special attention to the question of how various factors (mainly reducible to initial and boundary conditions) determine the shapes and sizes of the structures which develop. In this way, the role of order and disorder in flow patterns, as a factor strongly affecting the character of the evolution of structures, is revealed. The presentation emphasizes the physical picture of these phenomena, without excessive mathematical detail. Contents:Basic Concepts:The Boussinesq ApproximationThe Rayleigh-Bénard ProblemLinear AnalysisNonlinear Regimes and BifurcationsPlanforms of Convection CellsInvestigation Tools:ExperimentTheoretical ApproachesBasic Types of Convective-Flow Structures:Two-Dimensional Rolls and Three-Dimensional CellsPatterns of Quasi-Two-Dimensional RollsConvection Textures. Roll-Pattern DefectsConvection-Regimes:Regime DiagramPhase TurbulenceSpiral-Defect ChaosSelection of the Wavenumbers of Convection Rolls:Wavenumbers in Experiments with Random Initial DisturbancesSearches for Universal Selection CriteriaStability of Two-Dimensional Roll FlowsLyapunov Functional and Selection“Selection Mechanisms”Peculiarities of Stratification and Vertical Structure of Convection:Effects of Strong Temperature Dependence of ViscosityPenetrative ConvectionSmall-Scale Motions in a Globally Unstable LayerAstro- and Geophysical Applications Readership: Specialists in nonlinear phenomena, hydrodynamic stability, thermophysics, astrophysics, atmospheric and oceanic physics, applied science and technology; graduate students in physics, mechanics and mathematics. keywords:Rayleigh-Bénard Convection;Thermal Convection;Horizontal Layer;Structures;Patterns;Regimes;Wavenumber Selection “There are no other texts covering similar ground and … this book will be especially useful to any graduate student who wishes to understand modern developments in the theory of convection.” Journal of Fluid Mechanics “… there is no denying that the convective regime of moderate amplitude, where pattern theory works well, is well worth a book of its own, and Getling's is of about the right thickness.” Physics Today “…written competently and authoritatively … by far the best available monograph on Rayleigh-Bénard convection.” European Journal of Mechanics