A Road to Randomness in Physical Systems - Eduardo M. R. A. Engel

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Sommaire:
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 Hopf's 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 Hopf's 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.