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02/92 02-013-01

52

Probability and Nonlinear Systems by R. Daniel Mauldin

Part I: Introduction

Excerpts from The Scottish Book

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

Problem 3. Random Homeomorphisms

Iteration of Maps, Strange Attractors, and Number Theory-An Ulamian Potpourri by Paul R. Stein

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107

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"

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?