Deterministic and Random Evolution


Jens Lorenz
Dept. of Mathematics and Statistics, The University of New Mexico, Albuquerque, NM, USA

Series: Mathematics Research Developments
BISAC: SCI027000

After Isaac Newton’s great success in celestial mechanics, a world view of determinism was held by many scientists in the 1700 and 1800’s. This ended with the development of quantum mechanics, which introduced randomness at a fundamental level of our understanding of nature. In this book, the author introduces basic mathematical concepts for deterministic and random evolution. Among these are stability, bifurcation, hysteresis, time scales, expected value and variance. The gambler’s ruin problem, growth processes in biology, and Ehrenfest’s urn model illustrate random evolutions. The author also uses mathematical concepts to briefly discuss the arrow of time, determinism and free will, and creation vs. evolution. (Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. Introduction

Chapter 2. Basic Concepts

Chapter 3. Deterministic Systems: Outline of Advanced Topics

Chapter 4. Planetary Motion

Chapter 5. Is Time Reversible?

Chapter 6. The Bernoulli Shift and the Logistic Map

Chapter 7. Evolution on Two Time-Scales

Chapter 8. Stability and Bifurcations

Chapter 9. Scripts

Chapter 10. Two Oscillators: Periodicity, Ergodicity, and Phase Locking

Chapter 11. The Gambler’s Ruin Problem

Chapter 12. Gambler’s Ruin: Probabilities and Expected Time

Chapter 13. Stochastic Model of a Simple Growth Process

Chapter 14. Introduction to Kinetic Theory

Chapter 15. Random Evolution: From Order to Chaos



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