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2 183 kr
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The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri ous introduction to the subject. Of course, the meaning of "simplicity" varies from person to person and from country to country. The word "introduction" contains even more ambiguity. To start reading this book, only a moder ate knowledge of linear algebra and calculus is required. Other preliminaries, qualified as "elementary" in modern mathematics, are explicitly formulated in the book. These include the Fredholm Alternative for linear systems and the multidimensional Implicit Function Theorem. Using these very limited tools, a framewo:k of notions, results, and methods is gradually built that allows one to read (and possibly write) scientific papers on bifurcations of nonlinear dynamical systems. Among other things, progress in the sciences means that mathematical results and methods that once were new become standard and routinely used by the research and development community. Hopefully, this edition of the book will contribute to this process. The book's structure has been kept intact. Most of the changes introduced reflect recent theoretical and software developments in which the author was involved. Important changes in the third edition can be summarized as follows. A new section devoted to the fold-flip bifurcation for maps has appeared in Chapter 9.
634 kr
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- Nyhet
Dynamical Systems Essentials
An Application Oriented Introduction to Ideas, Concepts, Examples, Methods, and Results
Inbunden, Engelska, 2026
721 kr
Kommande
This textbook offers a rigorous yet accessible introduction to the qualitative theory of dynamical systems, focusing on both discrete- and continuous-time systems—those defined by iterated maps and differential equations. With clarity and precision, it provides a conceptual framework and the essential tools needed to describe, analyze, and understand the behavior of real-world systems across the sciences and engineering. Designed for advanced undergraduates and early graduate students, the book assumes only a foundational background in analysis, linear algebra, and differential equations. It bridges the gap between introductory courses and more advanced treatments by offering a self-contained and balanced approach—one that integrates geometric intuition with analytical rigor. Key features include:A carefully curated selection of topics essential for applied contextsFull, detailed proofs of cornerstone results, including the Poincaré-Bendixson theorem, Lyapunov’s stability criteria, Grobman-Hartman theorem, Center Manifold theoremA unified treatment of discrete- and continuous-time systems, with discrete methods often paving the way for their continuous counterpartsEmploying modern functional analytic techniques to streamline and clarify complex argumentsSpecial attention to invariant manifolds, symbolic dynamics, and topological normal forms for codimension-one bifurcations Whether for students planning further study in pure or applied mathematics, or for those in disciplines such as physics, biology, or engineering seeking to apply dynamical systems theory in practice, this book offers a concise yet comprehensive entry point. Instructors will appreciate its modular structure and completeness, while students will benefit from its clarity, rigor, and insightful presentation.