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• catalog abstract "In recent years there has been an explosive growth in the study of physical, biological, and economic systems that can be profitably studied using densities. Because of the general inaccessibility of the mathematical literature to the nonspecialist, little diffusion of the applicable mathematics into the study of these "chaotic" systems has taken place. This book will help bridge that gap. To show how densities arise in simple deterministic systems, the authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from many fields to illustrate the utility of the concepts and techniques presented, and the ideas in this book should thus prove useful in the study of a number of applied sciences. The authors assume that the reader has a knowledge of advanced calculus and differential equations. Basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed. Physicists, chemists, and biomathematicians studying chaotic behavior will find this book of value. It will also be a useful reference or text for mathematicians and graduate students working in ergodic theory and dynamical systems.".
• catalog contributor b5415486.
• catalog contributor b5415487.
• catalog contributor b5415488.
• catalog created "c1994.".
• catalog date "1994".
• catalog date "c1994.".
• catalog dateCopyrighted "c1994.".
• catalog description "1. Introduction -- 2. The Toolbox -- 3. Markov and Frobenius-Perron Operators -- 4. Studying Chaos with Densities -- 5. The Asymptotic Properties of Densities -- 6. The Behavior of Transformations on Intervals and Manifolds -- 7. Continuous Time Systems: An Introduction -- 8. Discrete Time Processes Embedded in Continuous Time Systems -- 9. Entropy -- 10. Stochastic Perturbation of Discrete Time Systems -- 11. Stochastic Perturbation of Continuous Time Systems -- 12. Markov and Foias Operators.".
• catalog description "In recent years there has been an explosive growth in the study of physical, biological, and economic systems that can be profitably studied using densities. Because of the general inaccessibility of the mathematical literature to the nonspecialist, little diffusion of the applicable mathematics into the study of these "chaotic" systems has taken place. This book will help bridge that gap. To show how densities arise in simple deterministic systems, the authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from many fields to illustrate the utility of the concepts and techniques presented, and the ideas in this book should thus prove useful in the study of a number of applied sciences. The authors assume that the reader has a knowledge of advanced calculus and differential equations. Basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed. Physicists, chemists, and biomathematicians studying chaotic behavior will find this book of value. It will also be a useful reference or text for mathematicians and graduate students working in ergodic theory and dynamical systems.".
• catalog description "Includes bibliographical references (p. [449]-456) and index.".
• catalog extent "xiv, 472 p. :".
• catalog hasFormat "Chaos, fractals, and noise.".
• catalog identifier "0387940499 (New York : acid-free paper)".
• catalog identifier "3540940499 (Berlin : acid-free paper)".
• catalog isFormatOf "Chaos, fractals, and noise.".
• catalog isPartOf "Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 97.".
• catalog isPartOf "Applied mathematical sciences ; v. 97".
• catalog issued "1994".
• catalog issued "c1994.".
• catalog language "eng".
• catalog publisher "New York : Springer-Verlag,".
• catalog relation "Chaos, fractals, and noise.".
• catalog subject "510 s 003/.75 20".
• catalog subject "Chaotic behavior in systems.".
• catalog subject "Probabilities.".
• catalog subject "QA1 .A647 vol. 97 QA402".
• catalog subject "System analysis.".
• catalog tableOfContents "1. Introduction -- 2. The Toolbox -- 3. Markov and Frobenius-Perron Operators -- 4. Studying Chaos with Densities -- 5. The Asymptotic Properties of Densities -- 6. The Behavior of Transformations on Intervals and Manifolds -- 7. Continuous Time Systems: An Introduction -- 8. Discrete Time Processes Embedded in Continuous Time Systems -- 9. Entropy -- 10. Stochastic Perturbation of Discrete Time Systems -- 11. Stochastic Perturbation of Continuous Time Systems -- 12. Markov and Foias Operators.".
• catalog title "Chaos, fractals, and noise : stochastic aspects of dynamics / Andrzej Lasota, Michael C. Mackey.".
• catalog type "text".