Cover for Lectures in Nonlinear Mechanics and Chaos Theory. Credit: World Scientific.22 Aug 2016 Singapore -

The first person to realize this was the French mathematician Henri Poincaré. In the late 19th century he was challenged to prove that the solar system is stable, but instead raised the possibility that it might not be. If one ignores the gravitational attraction between the planets one is left with a solvable problem that appears in all undergraduate mechanics texts. Including these small perturbations leads to a problem that can be described with partial differential equations, but these equations have no proper solutions except possibly in terms of infinite series.

These equations can be solved numerically of course, but the results show an odd combination of order and unpredictability. Henri Poincaré went on to lay the foundation for the study of such systems. He identified criteria that make a system inescapably chaotic and showed how a kind of order can emerge from the chaos. In this century, the Russian mathematician Kolomogrov developed what has come to be called the KAM theorem; one of the crowning works of modern mathematics. He showed that there is an odd fractal-like landscape of infinite series solutions in otherwise unsolvable problems.

"Lectures in Nonlinear Mechanics and Chaos Theory" begins by reviewing the tools of traditional classical mechanics - the Hamiltonian formulation, abstract transformation theory, and perturbation theory - and shows how they ultimately fail. It then moves on to the landmarks of chaos theory, the Poincaré-Hopf or "hairy ball" theorem, followed by the Poincaré-Birkoff theorem for rational winding numbers, and finally, the KAM theorem. These are discussed in terms of rigorous mathematics and illustrated with numerous examples of computer-drawn solutions. It finishes with a discussion of the relevance of the KAM theorem and measure theory to the ergodic hypothesis.

This book is based on a one-quarter course in graduate mechanics that has been given in the Physics Department of Oregon State University. It is intended to be used as a textbook to review conventional mechanics and introduce students to more recent developments in chaos theory.

This book retails for US$35 / GBP29 (paperback) and US$70 / GBP58 (hardback), and is also available on Amazon, Barnes and Noble, and other major online booksellers. To know more about the book or to purchase a copy, you can visit the World Scientific website.

World's biggest telescope meets world's second fastest supercomputer ...

NSF awards $110 million for advanced cyberinfrastructure to nation's scientists and engineers ...

Artificial atom created in graphene ...

Next steps in understanding brain function ...

New approach to computing boosts energy efficiency ...

Silicon nanoparticles trained to juggle light ...

Avere Systems and Cycle Computing provide one-click Cloud compute scalability ...

SCinet Inventory: High performance storage - untangling 89 miles of fiber ...

New microchip demonstrates efficiency and scalable design ...

Programmable routers could enable more resilient networks ...

Chaos could provide the key to enhanced wireless communications ...

Secure networks for the Internet of the future ...

IDT and IBM develop high-performance computing solution for telecom edge computing networks ...

ACM Gordon Bell Prize recognizes top accomplishments in running science apps on HPC ...

Insights into the dawn of the universe ...

Reef castaways: Can coral make it across Darwin's impassable barrier? ...

RAND and Lawrence Livermore National Lab combine computing & public policy analysis ...

Problems in mechanics open the door to the orderly world of chaos ...

New approach to determining how atoms are arranged in materials ...

Post-disaster optimization technique capable of analyzing entire cities ...

PPPL and Princeton help lead centre for study of runaway electrons ...

NSF funds new integrative approaches to study the brain ...

Streamlining accelerated computing for industry ...

Finalists compete for prestigious ACM Gordon Bell Prize in High Performance Computing ...

IBM expands all-flash storage offerings for Cloud and cognitive computing ...