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.
2.2.5. Application: Heron of Alexandria 33 2.3. Interval Maps 35 2.3.1. Cobwebbing 35 2.3.2. Fixed point stability 36 2.3.3. Monotonic maps 40 2.3.4. Homoclinic/heteroclinic points 42 2.4. First Return Maps 46 2.5. A Quadratic Interval Map: The Logistic Map 49 ... abstract dynamical system, (2) advanced enough that the course can utilize the ...
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