Dynamics outside the hyperbola of consistency - An overall geometric and probabilistic perspective

Author: Bonatti
Publisher:
Publish Date: 2007-01-01
Features: This book was led by Leo Moser and took 25 years to complete, featuring over 500 attractive open problems. Understanding many of these problems does not require extensive preparation knowledge. Each chapter is largely self-contained, outlining discrete geometry and introducing the historical details and important related results of each problem. This book can serve as a reference for professional mathematicians and graduate students dedicated to mathematical research, who love beautiful mathematical problems and tirelessly attempt to solve them. In the past 20 years, another major change has occurred in the theory of dynamical systems: researchers have attempted to establish a unified theory suitable for most "dynamical systems." Under this theory, as many conclusions as possible for the consistent hyperbolic case still hold. This book attempts to start from the latest advances and provide a unified overview of the theory of dynamical systems, proposing some open problems and pointing out possible future directions. It is aimed at beginners and researchers who wish to quickly and broadly understand this aspect of dynamics, discussing the main ideas, methods, and results at varying depths, along with relevant references, from which readers can obtain detailed information and supplementary material. The book consists of 12 chapters, each maintaining a considerable degree of independence to facilitate the reading of specific topics.