Nonlinear and Chaotic Maps

The following sections are included:

• One-Dimensional Maps

  • Exact and Numerical Trajectories

  • Fixed Points and Stability

  • Invariant Density

  • Liapunov Exponent

  • Autocorrelation Function

  • Discrete Fourier Transform

  • Fast Fourier Transform

  • Logistic Map and Liapunov Exponent for r ε [3,4]

  • Logistic Map and Bifurcation Diagram

  • Random Number Map and Invariant Density

  • Random Number Map and Random Integration

  • Circle Map and Rotation Number

  • Newton Method

  • Feigenbaum's Constant

  • Symbolic Dynamics

• Two-Dimensional Maps

  • Introduction

  • Phase Portrait

  • Fixed Points and Stability

  • Liapunov Exponents

  • Correlation Integral

  • Capacity

  • Hyperchaos

  • Domain of Attraction

  • Newton Method in the Complex Domain

  • Newton Method in Higher Dimensions

  • Ruelle-Takens-Newhouse Scenario

  • JPEG file