Introducing Chaos


Book Description

If a butterfly flaps its wings in Brazil, does it cause a tornado in Texas? Chaos theory attempts to answer such baffling questions. The discovery of randomness in apparently predictable physical systems has evolved into a science that declares the universe to be far more unpredictable than we have ever imagined. Introducing Chaos explains how chaos makes its presence felt in events from the fluctuation of animal populations to the ups and downs of the stock market. It also examines the roots of chaos in modern maths and physics, and explores the relationship between chaos and complexity, the unifying theory which suggests that all complex systems evolve from a few simple rules. This is an accessible introduction to an astonishing and controversial theory.




Introduction to Chaos


Book Description

This book focuses on explaining the fundamentals of the physics and mathematics of chaotic phenomena by studying examples from one-dimensional maps and simple differential equations. It is helpful for postgraduate students and researchers in mathematics, physics and other areas of science.




Chaos


Book Description

Chaos exists in systems all around us. This introduction draws in philosophy, literature, and maths to explain Chaos Theory, showing the variety of its applications in the real world, from technology to global warming, politics, and even gambling on the stock market.




Differential Equations, Dynamical Systems, and an Introduction to Chaos


Book Description

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.




Chaos: A Mathematical Introduction


Book Description

Textbook on chaos; class-tested, elementary but rigorous, with applications and lots of pictures and exercises.




Chaos


Book Description

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.







Quantum Chaos


Book Description

Discusses quantum chaos, an important area of nonlinear science.




Introduction to Random Chaos


Book Description

Introduction to Random Chaos contains a wealth of information on this significant area, rooted in hypercontraction and harmonic analysis. Random chaos statistics extend the classical concept of empirical mean and variance. By focusing on the three models of Rademacher, Poisson, and Wiener chaos, this book shows how an iteration of a simple random principle leads to a nonlinear probability model- unifying seemingly separate types of chaos into a network of theorems, procedures, and applications. The concepts and techniques connect diverse areas of probability, algebra, and analysis and enhance numerous links between many fields of science. Introduction to Random Chaos serves researchers and graduate students in probability, analysis, statistics, physics, and applicable areas of science and technology.




Call Sign Chaos


Book Description

#1 NEW YORK TIMES BESTSELLER • A clear-eyed account of learning how to lead in a chaotic world, by General Jim Mattis—the former Secretary of Defense and one of the most formidable strategic thinkers of our time—and Bing West, a former assistant secretary of defense and combat Marine. “A four-star general’s five-star memoir.”—The Wall Street Journal Call Sign Chaos is the account of Jim Mattis’s storied career, from wide-ranging leadership roles in three wars to ultimately commanding a quarter of a million troops across the Middle East. Along the way, Mattis recounts his foundational experiences as a leader, extracting the lessons he has learned about the nature of warfighting and peacemaking, the importance of allies, and the strategic dilemmas—and short-sighted thinking—now facing our nation. He makes it clear why America must return to a strategic footing so as not to continue winning battles but fighting inconclusive wars. Mattis divides his book into three parts: Direct Leadership, Executive Leadership, and Strategic Leadership. In the first part, Mattis recalls his early experiences leading Marines into battle, when he knew his troops as well as his own brothers. In the second part, he explores what it means to command thousands of troops and how to adapt your leadership style to ensure your intent is understood by your most junior troops so that they can own their mission. In the third part, Mattis describes the challenges and techniques of leadership at the strategic level, where military leaders reconcile war’s grim realities with political leaders’ human aspirations, where complexity reigns and the consequences of imprudence are severe, even catastrophic. Call Sign Chaos is a memoir of a life of warfighting and lifelong learning, following along as Mattis rises from Marine recruit to four-star general. It is a journey about learning to lead and a story about how he, through constant study and action, developed a unique leadership philosophy, one relevant to us all.