Textbook in PDF format

Until recently, measurable dynamics has been held as a highly theoretical mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution.
This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures, and transport problems.
The new and fast-developing computational tools discussed throughout the book allow for detailed analysis of real-world problems that are simply beyond the reach of traditional methods.
Front Matter
Dynamical Systems, Ensembles, and Transfer Operators
Dynamical Systems Terminology and Definitions
Frobenius—Perron Operator and Infinitesimal Generator
Graph Theoretic Methods and Markov Models of Dynamical Transport
Graph Partition Methods and Their Relationship to Transport in Dynamical Systems
The Topological Dynamics Perspective of Symbol Dynamics
Transport Mechanism, Lobe Dynamics, Flux Rates, and Escape
Finite Time Lyapunov Exponents
Information Theory in Dynamical Systems
Appendix A: Computation, Codes, and Computational Complexity
Back Matter