Author | Engel, Eduardo M. R. A. author |
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Title | A Road to Randomness in Physical Systems [electronic resource] / by Eduardo M. R. A. Engel |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1992 |
Connect to | http://dx.doi.org/10.1007/978-1-4419-8684-9 |
Descript | IX, 155 p. online resource |
1 Introduction -- 1.1 The Simple Harmonic Oscillator -- 1.2 Philosophical Interpretations -- 1.3 Coupled Harmonic Oscillators -- 1.4 Mathematical Results -- 1.5 Calculating Rates of Convergence -- 1.6 Hopfโs Approach -- 1.7 Physical and Statistical Independence -- 1.8 Statistical Regularity of a Dynamical System -- 1.9 More Applications -- 2 Preliminaries -- 2.1 Basic Notation -- 2.2 Weak-star Convergence -- 2.3 Variation Distance -- 2.4 Sup Distance -- 2.5 Some Concepts from Number Theory -- 3 One Dimensional Case -- 3.1 Mathematical Results -- 3.2 Applications -- 4 Higher Dimensions -- 4.1 Mathematical Results -- 4.2 Applications -- 5 Hopfโs Approach -- 5.1 Force as a Function of Only Velocity: One Dimensional case -- 5.2 Force as a Function of Only Velocity: Higher Dimensions -- 5.3 The Force also Depends on the Position -- 5.4 Statistical Regularity of a Dynamical System -- 5.5 Physical and Statistical Independence -- 5.6 The Method of Arbitrary Functions and Ergodic Theory -- 5.7 Partial Statistical Regularity -- 6 Non Diagonal Case -- 6.1 Mathematical Results -- 6.2 Linear Differential Equations -- 6.3 Automorphisms of the n-dimensional Torus -- References