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This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. This first volume is devoted to the analysis of dynamical systems with emphasis on problems of uncertainty, whereas the second volume will be devoted to control. It combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. It is accessible to mathematics students after two years of mathematics and graduate engineering students specializing in mathematical systems theory. The reader is gradually brought to the frontiers of research in stability and robustness analysis. As such the book will be useful for established researchers in systems theory as well as mathematicians and engineers interested in the mathematical foundations of systems and control. From the reviews: "This textbook on finite-dimensional time-invariant linear systems theory ... links up with the extensive research contributions of the authors, geared towards developing a spectral theory for uncertain systems. ... is bound to become a standard textbook and reference in its area." M. Kawski, Mathematical Reviews, 2005 "... the content ranges from rigorous proofs of basic results in linear systems theory to new results on the research frontier. In that sense, the book also serves as a valuable research reference." W.J. Satzer, MathDL, May, 2005 "I heartily recommend this book as a remarkably complete reference for researchers doing theoretical work involving linear systems. The book is a unique compilation of the mathematics underlying the field, and I look forward to seeing the authors' treatment of synthesis problems in the second volume." Brian Ingalls, IEEE Control Systems Magazine, April 2006 "MST-1 can be properly deemed an essential addition to the personal library of any researcher in systems theory. ...the authors indicate that MST-I was developed over a twenty-year period and the enormous effort that they have invested in writing the book is readily apoparent. MST-I is a superb exposition of advanced aspects of linear systems theory and is highly recommended for graduate students and researchers who have some prior background in control-systems and who have specific interests in problems of stability, robustness, and uncertainty. If the authors are able to maintain their high standards of exposition through the promised second volume, then MST-I and -II are destined to be placed among the pre-eminent authoritative references for the area of controlled dynamical systems." K.A. Grasse, IEEE Trans. Automatic Control 51, April 2006 "... This book is one of the best books on the subject." A.O. Ignatyev, Zentralblatt MATH 1074 :l.

Differentiable dynamical systems. --- Mathematical optimization. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppression-enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppression-enhancement of the initial chaos. The important applications of the theory presented in the book include: (1) control of chaotic escape from a potential well; (2) suppression of chaos in a driven Josephson junction; (3) control of chaotic solitons in Frenkel-Ko

Chaotic behavior in systems. --- Differentiable dynamical systems. --- Nonlinear control theory. --- Control theory --- Nonlinear theories --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- System theory

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From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).

Chaotic behavior in systems --- Quantum theory --- Chaos --- Congresses. --- Congrès --- EPUB-LIV-FT LIVPHYSI SPRINGER-B --- Congresses --- Physics. --- Differentiable dynamical systems. --- Statistical physics. --- Physics, general. --- Dynamical Systems and Ergodic Theory. --- Complex Systems. --- Classical and Continuum Physics. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Statistical methods --- Dynamics. --- Ergodic theory. --- Dynamical systems. --- Continuum physics. --- Classical field theory --- Continuum physics --- Continuum mechanics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Chaotic dynamics

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In this book, methodology of dynamical systems theory is applied to investigate the physics of the large-scale ocean circulation. Topics include the dynamics of western boundary currents such as the Gulf Stream in the Atlantic Ocean and the Kurosio in the Pacific Ocean, the stability of the thermohaline circulation, and the El Niño/Southern Oscillation phenomenon in the Tropical Pacific. The book also deals with the numerical methods to apply bifurcation analysis on large-dimensional dynamical systems, with tens of thousands (or more) degrees of freedom, which arise through discretization of ocean and climate models. The novel approach to understand the phenomena of climate variability is through a systematic analysis of the solution structure of a hierarchy of models using these techniques. In this way, a connection between the results of the different models within the hierarchy can be established. Mechanistic description of the physics of the results is provided and, where possible, links with results of state-of-the-art ocean (and climate) models and observations are sought. The reader is expected to have a background in basic fluid dynamics and applied mathematics, although the level of the text sometimes is quite introductory. Each of the chapters is rather self-contained and many details of derivations are provided. Exercises presented at the end of each chapter make it a perfect graduate-level text. This book is aimed at graduate students and researchers in meteorology, oceanography and related fields who are interested in tackling fundamental problems in dynamical oceanography and climate dynamics.

Ocean circulation --- Differentiable dynamical systems. --- Mathematical models. --- El Niňo Current --- El Niño Current --- Oceanography. --- Electronic data processing. --- Climatology. --- Complex Systems. --- Numeric Computing. --- Atmospheric Sciences. --- Dynamical Systems and Ergodic Theory. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Oceanography, Physical --- Oceanology --- Physical oceanography --- Thalassography --- Earth sciences --- Marine sciences --- Ocean --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Automation --- Mathematical geography. --- Statistical physics. --- Dynamical systems. --- Numerical analysis. --- Atmospheric sciences. --- Dynamics. --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Atmospheric sciences --- Atmosphere --- Mathematical analysis --- Mathematical statistics --- Climate --- Climate science --- Climate sciences --- Science of climate --- Atmospheric science --- Statistical methods --- Corriente del Niño --- Holy Child Current --- Niño Current --- Ocean circulation - Mathematical models. --- El Niňo Current - Mathematical models.

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Besides turbulence there is hardly any other scientific topic which has been considered as a prominent scientific challenge for such a long time. The special interest in turbulence is not only based on it being a difficult scientific problem but also on its meaning in the technical world and our daily life. This carefully edited book comprises recent basic research as well as research related to the applications of turbulence. Therefore, both leading engineers and physicists working in the field of turbulence were invited to the iTi Conference on Turbulence held in Bad Zwischenahn, Germany 21st - 24th of September 2003. Discussed topics include, for example, scaling laws and intermittency, thermal convection, boundary layers at large Reynolds numbers, isotropic turbulence, stochastic processes, passive and active scalars, coherent structures, numerical simulations, and related subjects. .

Engineering. --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Fluids. --- Statistical physics. --- Dynamical systems. --- Vibration. --- Fluid mechanics. --- Engineering Fluid Dynamics. --- Vibration, Dynamical Systems, Control. --- Statistical Physics, Dynamical Systems and Complexity. --- Fluid- and Aerodynamics. --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Hydromechanics --- Continuum mechanics --- Cycles --- Mechanics --- Sound --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Mathematical statistics --- Hydraulics --- Hydrostatics --- Permeability --- Partial differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Construction --- Industrial arts --- Technology --- Statistical methods --- Turbulence. --- Turbulence --- Mathematics. --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics --- Hydraulic engineering. --- Differentiable dynamical systems. --- Differential equations, partial. --- Complex Systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Shore protection