Qualitative Dynamics and Chaos

Arnaldo Rodriguez-Gonzalez

Okt 2023 · Arnaldo Rodriguez-Gonzalez

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This largely self-contained textbook on qualitative dynamics and chaos is intended for a broad audience of readers who are interested in describing systems that change over time using a mathematically simple, but conceptually rigorous, framework centered around descriptive sequences of symbols. This framework also allows readers who may not have a large amount of mathematical training to develop an unambiguous understanding of the notion of chaos and related aspects of dynamical systems theory. Concepts and techniques are introduced in the first parts of the book, which are later expanded to more mathematically abstract ideas in the latter parts of the book.

For those who are already have some mathematical training, this text is intended to be an alternative to standard symbolic dynamics textbooks which both mildly generalizes their scope and specifically centers its discussion around dynamical systems theory aspects. It uses the notion of a "falsifiable system"—a type of set of infinite symbol sequences, which is an extension of both formal languages and symbolic dynamical systems—as a central conceptual link between the theory of formal languages and the study of chaos, and allows readers a method to identify chaos within such systems (and systems equivalent to them) by entirely graphical methods. The latter parts of the book then focus on how to apply these methods to understand the dynamics of more traditional, numerically-based systems.

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Arnaldo Rodriguez-Gonzalez is a dynamicist, specializing in topological dynamics and its applications to fluid dynamical systems. He received his Ph.D. in theoretical and applied mechanics from Cornell, where he worked on applications of dynamical systems theory to low-Reynolds number hydrodynamics, and a B.S. in mechanical engineering from the University of Puerto Rico at Mayagüez. He has previously worked as an intern on multiple research projects, such as modeling thermal control systems for LIGO’s gravitational-wave detectors, modeling liquid xenon hydrodynamics for the XENON dark matter detector, and modeling thermoelectric superconducting magnet phenomena for both Fermi National Accelerator Laboratory and Lawrence Berkeley National Laboratory. He is also passionate about teaching, and has received the H. D. Block Prize in 2019 and 2021 for excellence in teaching engineering mechanics at Cornell.

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