Undergraduate Workshop

Aug 9-14 2010

University of Texas at Austin



Many systems in nature have non-linear laws of evolution. It can happen that even simple laws of evolution can lead to a very complicated evolution. The goal of the workshop is to present some analytical and numerical methods that can lead to understanding of these phenomena.


A standard undergraduate course in differential equations and some ability to use computers. It will also be desirable to have some more mathematical maturity, such as a course in linear algebra or a course in real analyisis or topology.


There will be 4 daily hours of lectures by Profs. M. Capinski, and R. de la Llave and graduate assistants. The lectures will be supplemented by practices based on XPPAUT, OCTAVE (Feel free to download them in your computers).


There will be financial support for students to attend the course.

Students from U. Texas at Austin will receive an stipend. Students from outside Austin will receive lodging and a meal allowance.

Unfortunately, the period to apply to attend the worshop and to request finacial support expired June 20 2010

U.T. Austin Students should be aware that there are also fellowships for further study associated with the RTG grants. Information about this opportunity including application forms are here

All the above support opportunities are subject to citizenship/residency requirements.

Materials for the workshop:

Computer software

  • CAPD-tutorial (PDF format)
  • CAPD-tutorial (source in zip)
  • Octave online manual
  • Gnu Scientific Library online manual
  • B. Ermentrout "Tutorial on XPPAUT"
  • Kermit Sigmon "Matlab Primer"
  • Numerical recipes books on line and other books
  • Mathematical Readings

  • M. Gidea, C.P. Niculescu "Chaotic dynamical systems: an introductioni"
  • E. N. Lorenz, "Deterministic nonperiodic flow"
  • J. Kennedy, J. A. Yorke "A chaos lemma"
  • J. Kennedy, J. A. Yorke "Topological horseshoes"
  • J. H. Hubbard "The Forced Damped Pendulum: Chaos, Complication and Control"
  • Jason James' notes on Celestial mechanics with Matlab examples.
  • Aug 9

    Some sample Fortran programs discussed in the lecture

    Aug 11

    Challenges in pdf and a zipped folder with sample files for the programs.

    Aug 12

    Challenges in pdf and a zipped folder with sample files for the programs.

    Partial solutions (hints) to the problems: Rossler equations and forced pendulum