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Dynamical Systems Essentials: An Application Oriented Introduction to Ideas, Concepts, Examples, Methods, and Results
Hardcover
Series: Texts in Applied Mathematics, Book 83
Technology & EngineeringGeneral MathematicsGeneral Science
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ISBN10: 3032040825
ISBN13: 9783032040824
Publisher: Springer
Published: May 12 2026
Pages: 391
Weight: 2.04
Height: 1.07 Width: 6.45 Depth: 9.34
Language: English
ISBN13: 9783032040824
Publisher: Springer
Published: May 12 2026
Pages: 391
Weight: 2.04
Height: 1.07 Width: 6.45 Depth: 9.34
Language: English
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 contexts Full, detailed proofs of cornerstone results, including the Poincaré-Bendixson theorem, Lyapunov's stability criteria, Grobman-Hartman theorem, Center Manifold theorem A unified treatment of discrete- and continuous-time systems, with discrete methods often paving the way for their continuous counterparts Employing modern functional analytic techniques to streamline and clarify complex arguments Special attention to invariant manifolds, symbolic dynamics, and topological normal forms for codimension-one bifurcations
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