Dynamical Systems Essentials: An Application Oriented Introduction to Ideas, Concepts, Examples, Methods, and Results (Texts in Applied Mathematics, 83)

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, Grobm