Dynamics Numerical Explorations [Hardcover]

Preface 1. Getting the program running 1.1 The Dynamics program and hardware Smalldyn: a small version of Dynamics 1.2 Getting started with Dynamics Using the mouse Appendix: description of the interrupts 1.3 Questions 2. Samples of Dynamics: pictures you can make simply 2.1 Introduction Example 2-1a: Plot a trajectory Example 2-1b: Draw a box Example 2-1c: Viewing the Parameter Menu Example 2-1d: Refresh the screen and continue plotting Example 2-1e: Clear the screen and continue plotting Example 2-1f: Single stepping through a trajectory Example 2-1g: Plot a cross at current position Example 2-1h: Draw axes and print picture Example 2-1i: Initializing Example 2-1j: Viewing the Y Vectors Example 2-1k: Find a fixed point Example 2-1l: Find a period 2 orbit Example 2-1m: Search for all periodic points of period 5 Example 2-1n: Change RHO Example 2-1o: Plotting permanent crosses Example 2-1p: Set storage vector y1 and initialize Example 2-1q: Change X Scale or Y Scale 2.2 Complex pictures that are simple to make Example 2-2a: Chaotic attractor Example 2-2b: Computing Lyapunov exponents Example 2-2c: Plotting trajectory versus time Example 2-3a: Graph of iterate of one dimensional map Example 2-3b: Cobweb plot of a trajectory Example 2-3c: Plotting trajectory versus time Example 2-4: The Henon attractor Example 2-5: The first iterate of a quadrilateral Example 2-6: Plotting direction field and trajectories Example 2-7: Bifurcation diagram for the quadratic map Example 2-8: Bifurcation diagram with bubbles Example 2-9: All the Basins and Attractors Example 2-10: Metamorphoses in the basin of infinity Example 2-11: Search for all periodic points with period 10 Example 2-12: Search for all period 1 and period 2 points Example 2-13: Following orbits as a parameter is varied Example 2-14: The Mandelbrot set Example 2-15: All the Basins and Attractors Example 2-16: 3-Dimensional views on the Lorenz attractor Example 2-17: Unstable manifold of a fixed point Example 2-18: Stabl³D