This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.

Can Jaxon Hampton love the Moon Queen enough to save Earth? If Zeth, the servant of her enemies the Shadow Giants, defeats Jaxon in battle, the Shadow Giants unleash chaos on Earth and destroy humanity. Every night Jaxon experiences vivid recurring dreams in which, 10,000 years ago, he escorts a beautiful woman through many dangers to the top of a cliff overlooking the Nile River. How come his boss's daughter dreams the same story? And why does a strange man hypnotize Jaxon to take the young woman to a bluff overlooking the Mississippi River during the next full moon? Jaxon works as head trader for a small money management business. His boss tells him she came up with a sure-fire trading system, the Chaos Formula. Her test account verifies a terrifyingly high number of winning trades. Jaxon can't believe. Stock market results form a random, bell-shaped curve. Perhaps not a strictly normal distribution, but unpredictable. Yet this ability of his boss to foretell stock market results constitutes just one sign of reality going haywire. What compels Jaxon to spend his evenings staring up at the moon, even to the point he forces his girlfriend to leave him? Every night, he dreams he wields a bronze sword ten thousand years in the past, at the mouth of the Nile River, long before the pyramids. He fights as a soldier for the king of a growing empire. The other soldiers call him Blood Reaper. One night the king assigns him to take a young woman far upriver, for a sacrifice. A strangely beautiful woman, despite her white skin, blue eyes, and gold hair. She must travel to where bluffs overlook the Nile River, protected only by Jaxon -- against roving animals, wild people, and superstitious dirt farmers. Jaxon does not understand why the sacrifice takes place so far from the temples, but he must obey his king. He figures a wealthy merchant wishes to sacrifice an ex-mistress to gain merit with the gods instead of just selling her to a brothel. When she reveals her true identity as the Moon Queen herself, he does not believe . . . until he meets her ancient enemies the Shadow Giants. How and why does his boss's daughter, Laura Ewing, dream the same story, only as the woman? And how can he and Laura use her mother's Chaos Formula to win over five hundred dollars at a Mini-Bac table at the Lumiere Place Casino? Why does Mr. bin Hasad, the small, dapper foreigner keep visiting Jaxon on his job even though he doesn't open up a trading account? And Jaxon can't remember what they discuss? How did Jaxon's brother Keith buy the most evil book in the world from Ken, the Romani and Bosnian refugee who runs the largest occult bookstore in the New World, when Keith claims he stops dealing drugs? Why does someone calling himself Zeth kill young women and drain their blood into a crystal bowl to scry messages to and from the Shadow Giants? Blood Reaper's story comes to a conclusion on top of the cliff overlooking the Nile River. Jaxon's story reaches its conclusion on top of a bluff overlooking the Mississippi River. Who lives? Who dies? Do the Shadow Giants overwhelm life on Earth with chaos and destruction? To find out, scroll up and download the dark fantasy adventure The Chaos Formula now. This paranormal fantasy adventure combines stories from ten thousand years ago -- a nitty gritty historical dark fantasy -- with a contemporary dark fantasy in the modern world. A form of urban fantasy as well.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron—Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly. The book contains many worked examples and over 250 exercises. While these exercises are accessible to students and have been class-tested, they also suggest further problems and possible research topics.

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.

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.