by Shou-Li Peng (Yunnan University, China) & Ke-Fei Cao (Yunnan University, China)

Universality in chaotic systems is one of the fascinating achievements of nonlinear science. For one-dimensional iterative systems, star products in symbolic dynamics are basic tools for obtaining universalities through renormalization. This book is a systematic and complete elaboration of star products in one-dimensional multimodal maps, explaining their algebraic and geometric meanings, establishing symbolic dynamics of equal topological entropy classes, and extracting the universality, global regularities and thermodynamics formalism of the dynamical quantities of systems. The book displays the strength and efficiency of the method of one-dimensional symbolic dynamics equipped with star products.

• Preliminaries: Symbolic Dynamics
• Symbolic Coordinate System
• Algebraic Formalism of Star Products
• Geometry of Star Products
• Equal Entropy Symbolic Dynamics
• Metric Universality and Star Products
• Global Regularities and Equal Entropy Class
• Thermodynamic Formalism of Dynamical Quantities