Dynamical systems essentials an application oriented introduction to ideas, concepts, examples, methods, and results Yuri Kuznetsov, Odo Diekmann, Wolf-Jürgen Beyn

Format:

Book

Author/Creator:

Kuznetsov, Yuri, author.

Diekmann, O., author.

Beyn, Wolf-Jürgen, author.

Series:

Texts in applied mathematics ; 2196-9949 83

Texts in Applied Mathematics 2196-9949 volume 83

Language:

English

Subjects (All):

Dynamics.

Differential equations.

Physical Description:

1 online resource

Place of Publication:

Cham Springer 2026

Summary:

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 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

Contents:

Introduction

Linear maps and ODEs

Local behavior of nonlinear systems

Planar ODE

etc

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed May 27, 2026)

Other Format:

Print version Kuznetsov, Yuri Dynamical Systems Essentials

ISBN:

9783032040831

3032040833

OCLC:

1592990794

Access Restriction:

Restricted for use by site license