Transcription of An Modern Introduction to Dynamical Systems
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An Modern Introduction to Dynamical Systems
An Modern Introduction toDynamical SystemsRichard J. BrownContentsPrefaceiiiChapter 1. What is a Dynamical System? Ordinary Differential Equations (ODEs) Symbolic Higher-order The viewpoint12 Chapter 2. Simple A simple The The Contraction Contractions on Contractions in several Application: Newton-Raphson Application: Existence and Uniqueness of ODE Application: Heron of Interval Fixed point Monotonic Homoclinic/heteroclinic First Return A Quadratic Interval Map: The Logistic More general metric The unit The The A Cantor The Koch Sierpinski Gasket:63 Chapter 3. Linear Maps Linear, First-order ODE Systems in the Local Linearization and Equilibria Linear Planar Sinks & Star Degenerate Spirals and The Matrix Application: Competing Species81 The Fixed Points,84 Type and 4.
ii CONTENTS 3.2. Local Linearization and Equilibria Stability 65 3.3. Linear Planar Maps 65 3.3.1. Sinks & sources 69 3.3.2. Star nodes 70 3.3.3. Degenerate Nodes 71
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