Dynamics: Numerical Explorations : Accompanying Computer Program Dynamics

The handbook Dynamics: Numerical Explorations describes how to use the program, Dynamics , to investigate dynamical systems. Co-author J.A. Yorke, while working with the Maryland Chaos Group, developed an array of tools to help visualize the properties of dynamical systems. Yorke found it useful to combine these various basic tools with each other into a single package. The resulting program is Dynamics which requires either a Unix workstation running X11 graphics or an IBM PC compatible computer. The program together with the manual Dynamics: Numerical Explorations provides an introduction to and an overview of fundamental, sophisticated tools and numerical methods together with many simple examples. All numerical methods described in this handbook are implemented in the program Dynamics . Some of the program's capabilities are: iterating maps and solving differential equations; plotting trajectories; featuring an array of simple commands; printing a created picture in resolution higher than that of the screen. Plotting trajectories is a useful capability in exploring a dynamical system, but it is just the beginning. The Maryland Chaos Group developed an array of tools to help visualize the properties of dynamical systems induding automatic method for plotting all "basins and attractors ", and for automatically searching for all computing "straddle trajectories", periodic orbits of a specified period. In the investigations of the Maryland Chaos Group, I.A. Yorke found it useful to be able to combine these various basic tools with each other into so that each new study could benefit a single package that grew with time from the previous programming efforts. He has been writing this software and distributing versions for the last nine years. The resulting program Dynamics requires either a Unix workstation running XII graphics or an IBM PC compatible computer. Eric I. Kostelich has put in a great deal of effort to port the program to Unix workstations. Some basic tools in Dynamics, such as the computation of Lyapunov exponents and the use of Newton's method are standard. The method of computation of stable and unstable manifolds is superior to standard procedures. Dynamics is currently being used extensively in our research and it is being used in undergraduate courses. Dynamics: Numerical Explora#ons provides an introduction to and overview of fundamental tools and numerical methods together with many simple examples. All the numerical methods described in this book are implemented in Dynamics Plotting trajectories is a useful capability in exploring a dynamical system, but it is just the beginning. The Maryland Chaos Group developed an array of tools to help visualize the properties of dynamical systems induding automatic method for plotting all'basins and attractors', and for automatically searching for all computing'straddle trajectories', periodic orbits of a specified period. In the investigations of the Maryland Chaos Group, I. A. Yorke found it useful to be able to combine these various basic tools with each other into so that each new study could benefit a single package that grew with time from the previous programming efforts. He has been writing this software and distributing versions for the last nine years. The resulting program Dynamics requires either a Unix workstation running XII graphics or an IBM PC compatible computer. Eric I. Kostelich has put in a great deal of effort to port the program to Unix workstations. Some basic tools in Dynamics, such as the computation of Lyapunov exponents and the use of Newton's method are standard. The method of computation of stable and unstable manifolds is superior to standard procedures. Dynamics is currently being used extensively in our research and it is being used in undergraduate courses. Dynamics: Numerical Explora#ons provides an introduction to and overview of fundamental tools and numerical methods together with many simple examples. All the numerical methods described in this book are implemented in Dynamics. Front Matter....Pages i-xiii Getting the Program Running....Pages 1-18 Samples of Dynamics : Pictures You Can Make Simply....Pages 19-124 Screen Utilities....Pages 125-166 Utilities....Pages 167-200 Dimension and Lyapunov Exponents....Pages 201-228 Bifurcation Diagrams....Pages 229-268 Basins of Attraction....Pages 269-314 Straddle Trajectories....Pages 315-346 Unstable and Stable Manifolds....Pages 347-370 Finding Periodic Orbits....Pages 371-390 Following Periodic Orbits....Pages 391-406 Changing the Program....Pages 407-432 Dynamics on Unix Systems....Pages 433-442 Appendix....Pages 443-458 References....Pages 459-466 Back Matter....Pages 467-485 This handbook describes how to use the software package Dynamics in order to investigate dynamical systems. The program may be used to iterate maps and solve differential equations, plot trajectories and print a created picture in a higher resolution than that of the computer screen. Allows the reader to explore nonlinear dynamics and chaos by the use of illustrated graphics. This title is suitable for research and educational needs. Chaotic dynamics has a long history that can be traced back to the papers of Henri Poincare and James Clerk Maxwell.