Applied and Computational Measurable Dynamics

Abstract

Until recently, measurable dynamics has been held as a highly theoretcal 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. Audience: Applied and Computational Measurable Dynamics is intended for advanced undergraduate and graduate students and researchers in applied dynamical systems, computational ergodic theory, geosciences, and fluid dynamics. Contents Chapter 1: Dynamical Systems, Ensembles, and Transfer Operators; Chapter 2: Dynamical Systems Terminology and Definitions; Chapter 3: Frobenius-Perron Operator and Infintesimal Generator; Chapter 4: Graph Theoretic Methods and Markov Models of Dynamical Transport; Chapter 5: Graph Partition Methods and Their Relationship to Transport in Dynamical Systems; Chapter 6: The Topological Dynamics Perspective of Symbol Dynamics; Chapter 7: Transport Mechanism, Lobe Dynamics, Flux Rates, and Escape; Chapter 8: Finite Time Lyapunov Exponents; Chapter 9: Information Theory in Dynamical Systems; Appendix A: Computation, Codes, and Computational Complexity; Bibliography; Index