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BL
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| Record Number
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854795
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| Title & Author
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Deterministic and random evolution /\ Jens Lorenz, editor.
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| Publication Statement
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[Hauppauge], New York :: Nova Science Publishers, Inc.,, [2013]
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| Series Statement
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Mathematics research developments
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| Page. NO
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1 online resource.
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| ISBN
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1626180202
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: 9781626180208
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1626180148
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9781626180147
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| Bibliographies/Indexes
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Includes bibliographical references (pages 183-184) and index.
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| Contents
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DETERMINISTIC AND RANDOM EVOLUTION; DETERMINISTIC AND RANDOM EVOLUTION; Library of Congress Cataloging-in-Publication Data; Contents; Preface; Chapter 1: Introduction; Chapter 2: Basic Concepts; 1. Initial Value Problems for ODEs; 2. Discrete-Time Dynamics; 3. Continuous vs. Discrete Time; 4. Random Evolution; 5. Discussion; Chapter 3: Deterministic Systems: Outline of Advanced Topics; 1. Planetary Motion: Example for Determinism; 2. Reversibility in Time; 3. Sensitive Dependence on Initial Conditions; 4. Averages; 5. Dependence on Parameters; 6. Variation on Different Time Scales.
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1. Probability of Ruin2. Probability of Winning; 3. Expected Time; 4. The Matrix View: Limit of Probability Densities; Chapter 13: Stochastic Model of a Simple Growth Process; 1. Growth Models; 2. The Forward Kolmogorov Equations; 3. Solution of the Forward Kolmogorov Equations; 4. The Sum of the pj(t); 5. The Expected Value of Xt; 6. The Variance of Xt; 7. Statistics of Interevent Times; 8. Numerical Realization of Random Evolution; 9. Figures and Scripts; Chapter 14: Introduction to Kinetic Theory; 1. Boyle, Bernoulli, Maxwell, and Sadi Carnot.
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2. The Bernoulli Shift: Dynamical Properties3. The Logistic Map and Its Relation to the Bernoulli Shift; 4. Average Behavior of the Logistic Map; Chapter 7: Evolution on Two Time-Scales; 1. Fast and Slow Time Scales; 2. Simple Example; 3. A Difficult Example; Chapter 8: Stability and Bifurcations; 1. Fixed Points; 2. Exponential Growth; 3. Logistic Growth; 4. The Delayed Logistic Map; 5. Parameter Dependent Evolution and Hysteresis; Chapter 9: Scripts; 1. Script for Logistic Growth; 2. Scripts for the Delayed Logistic Map; 3. Scripts for Parameter Dependent Evolution and Hysteresis.
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Chapter 10: Two Oscillators: Periodicity, Ergodicity, and Phase Locking1. The Circle and the Two-Torus; 2. Uncoupled Oscillators: Periodic Solutions; 3. Uncoupled Oscillators: Ergodicity; 4. Time Average Equals Space Average for a Circle Map; 5. Coupled Oscillators; Chapter 11: The Gambler's Ruin Problem; 1. Description of the Game; 2. Some Questions and Numerical Realization; 3. The Transition Matrix P; 4. Evolution of Probability Density; 5. Discussion; 6. Application; 7. Script: Evolving the Probability Density for Gambler's Ruin; Chapter 12: Gambler's Ruin: Probabilities and Expected Time.
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Chapter 4: Planetary Motion1. Outline; 2. The Two Body Problem: Reduction to One Body in a Central Field; 3. One Body in a Central Field; 4. The Equation for an Ellipse in Polar Coordinates; 5. The Kepler Orbit; 6. Kepler's Third Law; 7. Time Dependence; 8. Bessel Functions via a Generating Function: Integral Representation; 9. Discussion; Chapter 5: Is Time Reversible?; 1. Reversibility for the Two Body Problem; 2. Reversibility: General Definition; 3. Discussion; Chapter 6: The Bernoulli Shift and the Logistic Map; 1. The Bernoulli Shift: Definition.
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| Subject
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Evolution equations.
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Stochastic sequences.
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Evolution equations.
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| Subject
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MATHEMATICS-- Game Theory.
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| Subject
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Stochastic sequences.
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| Dewey Classification
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519.3
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| LC Classification
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QA274.225
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| Added Entry
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Lorenz, Jens,1949-
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