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Part II: A Tutorial on Probability, Measure, and the Laws of Large Numbers
Cantor's Middle-Third Set
Part III: Probabilistic Approaches to Nonlinear Problems
Problem 1. Energy Redistribution: An Exact Solution to a Nonlinear, Many-Particle System
Problem 2. Geometry, Invariant Measures, and Dynamical Systems
Poincaré's Proof of the Recurrence Theorem
PHYSICS
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52
Problem 3. Random Homeomorphisms
Iteration of Maps, Strange Attractors, and Number Theory—An Ulamian Potpourri by Paul R. Stein
91
Learning from Ulam: Measurable Cardinals, Ergodicity, and Biomathematics by Jan Mycielski
The Existence and Significance of Ergodic Transformations-Excerpts from the Introduction to
Oxtoby and Ulam's “Measure-Preserving Homeomorphisms and Metrical Transitivity"
107
The Ergodic Hypothesis: A Complicated Problem of Mathematics and Physics by Adrian Patrascioiu 263
The FPU Problem: Excerpts from "Studies of Nonlinear Problems" by Fermi, Pasta, and Ulam
Does Equipartition of Energy Occur in Nonlinear Continuous Systems?